Posted:December 10, 2017

Mouse Light Multi-disciplinary Team is Unlocking the Connected Secrets of Neurons

An amazing multi-disciplinary team of about 40 neurobiological and computer scientists and technicians is systematically cataloging, tracing and visualizing neurons in the mouse brain. The effort, called MouseLight, is funded by the Howard Hughes Medical Institute and is conducting the work at HHMI’s spectacular Janella Research Campus in Virginia. MouseLight is generating maps of individual neurons across the entire mouse brain using high-speed, high-resolution light microscopy. So far, 300 neurons have been painstakenly completed, with a target of 1000 by the end of 2018. While impressive, there is still a considerable ways to go to capture all of the estimated 70 million! neurons in the mouse brain.

The visualizations of the neurons, singly and in combination, are just amazing. For example, according to a recent project news release, some “axons of individual neurons in the thalamus often branch profusely in unexpected combinations of cortical areas, such as regions involved in taste, touch, and movement. Similarly, in the subiculum, a region involved in learning and memory, neurons almost always reach out to a few different places. In the neocortex, the six-layered structure associated with the highest cognitive functions, many single-neuron projections spread expansively. One neuron the researchers traced ran scattershot across the cerebral cortex, sending long, branching axons arcing across both hemispheres like a fireworks explosion.”

At the project’s Web site you can see an introductory video and use an interactive Neuron Browser, which allows you to select and view and manipulate specific neurons, including a nice tutorial and pre-canned examples:

Mouse Light Video

Only one to a few neurons may be processed at a time to generate the primary data underlying all of this analysis. The basic process works as follows: First, the researchers inject the mouse brain with a virus that highlights those few neurons. The brain is then excised and ‘cleared’ to enable light to penetrate the tissue. The brain is hit with a pulse of light to illuminate the target neurons using ‘two-photon microscopy’ to get the sharp images needed to identify the specific neurons, and then sliced (‘microtomed’) into 200-micrometer thick layers with a vibrating razor. After digitizing the image on the slice, the process is repeated until the entire brain is characterized. The digitized, illuminated areas on each slice are then re-constructed by computer with trained annotators tracing and confirming the actual neuron trace. Each processing of a few neurons yields approximately 20 terabytes of data. Neurons on the combined datasets are then color-coded, and are processed by 3-D visualization software for animations and rotations. The software, as demonstrated by the online browser, enables specific neurons to be turned on or off for inspection and other 3-D manipulations. As the team has continued to learn, it has continued to speed up the process.

These kinds of advances are now giving us an unprecedented look at the physical structure and connectedness of neurons. For those of us doing knowledge representation and digital cognition work, and if we believe ultimately our work needs to be a reflection of physical reality in some form, we are apparently still a long, long ways away from being able to model animate brain functions. The degrees of connectivity suggested are staggering, and well short of current practice in any digital artifact. One of the next challenges for neuroscience is to try to discover physical patterns of connections that shed light on generalizations, for it looks like, based on these early physical findings, that the brain is an unbelievably jumbled mess of pathways and connections. Finding general keys will be needed to unlock the mysteries.

Posted:November 22, 2017

Keel-billed ToucanKnowledge Representation Guidelines from Charles S. Peirce

‘Representation’ is the second half of knowledge representation (KR), the field of artificial intelligence dedicated to representing information about the world in a form that a computer system can utilize to solve complex tasks. One dictionary sense is that ‘representation’ is the act of speaking or acting on behalf of someone else; this is the sense, say, of a legislative representative. Another sense is a statement made to some formal authority communicating an assertion, opinion or protest, such as a notarized document. The sense applicable to KR, however, according to the Oxford Dictionary of English, is one of ‘re-presenting’. That is, “the description or portrayal of someone or something in a particular way or as being of a certain nature” [1]. In this article I investigate this sense of ‘re-presenting’ following the sign-making guidelines of Charles Sanders Peirce [2] [3] (which we rely upon in our KBpedia knowledge structure).

When we see something, or point to something, or describe something in words, or think of something, we are, of course, using proxies in some manner for the actual thing. If the something is a ‘toucan’ bird, that bird does not actually reside in our head when we think of it. The ‘it’ of the toucan is a ‘re-presentation’ of the real, dynamic toucan. The representation of something is never the actual something, but is itself another thing that conveys to us the idea of the real something. In our daily thinking we rarely make this distinction, thankfully, otherwise our flow of thoughts would be completely jangled. Nonetheless the distinction is real, and when inspecting the nature of knowledge representation, needs to be consciously considered.

How we ‘re-present’ something is also not uniform or consistent. For the toucan bird, perhaps we make caw-caw bird noises or flap our arms to indicate we are referring to a bird. Perhaps we simply point at the bird. Or, perhaps we show a picture of a toucan or read or say aloud the word “toucan” or see the word embedded in a sentence or paragraph, as in this one, that also provides additional context. How quickly or accurately we grasp the idea of toucan is partly a function of how closely associated one of these signs may be to the idea of toucan bird. Probably all of us would agree that arm flapping is not nearly as useful as a movie of a toucan in flight or seeing one scolding from a tree branch.

The question of what we know and how we know it fascinated Peirce over the course of his intellectual life. He probed this relationship between the real or actual thing, the object, with how that thing is represented and understood. This triadic relationship between object, representation and interpretation forms a sign, and is the basis for the process of sign-making and understanding, which Peirce called semiosis [4]. Peirce’s basic sign relationship is central to his own epistemology and resides at the core of how we use knowledge representation in KBpedia.

The Shadowy Object

Yet even the idea of the object, in this case the toucan bird, is not necessarily so simple. There is the real thing itself, the toucan bird, with all of its characters and attributes. But how do we ‘know’ this real thing? Bees, like many insects, may perceive different coloration for the toucan and adjacent flowers because they can see in the ultraviolet spectrum, while we do not. On the other hand, most mammals in the rain forest would also not perceive the reds and oranges of the toucan’s feathers, which we readily see. Perhaps only fellow toucans could perceive by gestures and actions whether the object toucan is healthy, happy or sad (in the toucan way). Humans, through our ingenuity, may create devices or technologies that expand our standard sensory capabilities to make up for some of these perceptual gaps, but technology will never make our knowledge fully complete. Given limits to perceptions and the information we have on hand, we can never completely capture the nature of the dynamic object, the real toucan bird.

Then, of course, whatever representation we have for the toucan is also incomplete, be it a mental image, a written description, or a visual image (again, subject to the capabilities of our perceptions). We can point at the bird and say “toucan”, but the immediate object that it represents still is different than the real object. Or, let’s take another example more in keeping with the symbolic nature of KR, in this case the word for ‘bank’. We can see this word, and if we speak English, even recognize it, but what does this symbol mean? A financial institution? The shore of a river? Turning an airplane? A kind of pool shot? Tending a fire for the evening? In all of these examples, there is an actual object that is the focus of attention. But what we ‘know’ about this object depends on what we perceive or understand and who or what is doing the perceiving and the understanding. We can never fully ‘know’ the object because we can never encompass all perspectives and interpretations.

Peirce well recognized these distinctions. He termed the object of our representations the immediate object, while also acknowledging this representation is not fully capturing of the underlying, real dynamical object:

“Every cognition involves something represented, or that of which we are conscious, and some action or passion of the self whereby it becomes represented. The former shall be termed the objective, the latter the subjective, element of the cognition. The cognition itself is an intuition of its objective element, which may therefore be called, also, the immediate object.” (CP 5.238)

“Namely, we have to distinguish the Immediate Object, which is the Object as the Sign itself represents it, and whose Being is thus dependent upon the Representation of it in the Sign, from the Dynamical Object, which is the Reality which by some means contrives to determine the Sign to its Representation.” (CP 4.536)

“As to the Object, that may mean the Object as cognized in the Sign and therefore an Idea, or it may be the Object as it is regardless of any particular aspect of it, the Object in such relations as unlimited and final study would show it to be. The former I call the Immediate Object, the latter the Dynamical Object.” (CP 8.183)

Still, we can not know anything without the sign process. One imperative of knowledge representation — within reasonable limits of time, resources and understanding — is to try to ensure that our immediate representation of the objects of our discourse are in as close a correspondence to the dynamic object as possible. This imperative, of course, does not mean assembling every minute bit of information possible in order to characterize our knowledge spaces. Rather, we need to seek a balance between what and how we characterize the instances in our domains with the questions we are trying to address, all within limited time and budgets. Peirce’s pragmatism, as expressed through his pragmatic maxim, helps provide guidance to reach this balance.

Three Modes of Representation

Representations are signs (CP 8.191), and the means by which we point to, draw or direct attention to, or designate, denote or describe a particular object, entity, event, type or general. A representational relationship has the form of re:A. Representations can be designative of the subject, that is, be icons or symbols (including labels, definitions, and descriptions). Representations may be indexes that more-or-less help situate or provide traceable reference to the subject. Or, representations may be associations, resemblances and likelihoods in relation to the subject, more often of indeterminate character.

In Peirce’s mature theory of signs, he characterizes signs according to different typologies, which I discuss further in the next section. One of his better known typologies is how we may denote the object, which, unlike some of his other typologies, he kept fairly constant throughout his life. Peirce formally splits these denotative representations into three kinds: icons, indexes, or symbols (CP 2.228, CP 2.229 and CP 5.473).

“. . . there are three kinds of signs which are all indispensable in all reasoning; the first is the diagrammatic sign or icon, which exhibits a similarity or analogy to the subject of discourse; the second is the index, which like a pronoun demonstrative or relative, forces the attention to the particular object intended without describing it; the third [or symbol] is the general name or description which signifies its object by means of an association of ideas or habitual connection between the name and the character signified.” (CP 1.369)

The icon, which may also be known as a likeness or semblance, has a quality shared with the object such that it resembles or imitates it. Portraits, logos, diagrams, and metaphors all have an iconic denotation. Algebraic expressions are also viewed by Peirce as icons, since he believed (and did much to prove) that mathematical operations can be expressed through diagrammatic means (as is the case with his later existential graphs).

An index denotes the object by some form of linkage or connection. An index draws or compels attention to the object by virtue of this factual connection, and does not require any interpretation or assertion about the nature of the object. A pointed finger to an object or a weathervane indicating which direction the wind is blowing are indexes, as are keys in database tables or Web addresses (URIs or URLs [5]) on the Internet. Pronouns, proper names, and figure legends are also indexes.

Symbols, the third kind of denotation, represent the object by virtue of accepted conventions or ‘laws’ or ‘habits’ (Peirce’s preferred terms). There is an understood interpretation, gained through communication and social consensus. All words are symbols, plus their combinations into sentences and paragraphs. All symbols are generals, but which need to be expressed as individual instances or tokens. For example, ‘the’ is a single symbol (type), but it is expressed many times (tokens) on this page. Knowledge representation, by definition, is based on symbols, which need to be interpreted by either humans or machines based on the conventions and shared understandings we have given them.

Peirce confined the word representation to the operation of a sign or its relation to the interpreter for an object. The three possible modes of denotation — that is, icon, index or symbol — Peirce collectively termed the representamen:

“A very broad and important class of triadic characters [consists of] representations. A representation is that character of a thing by virtue of which, for the production of a certain mental effect, it may stand in place of another thing. The thing having this character I term a representamen, the mental effect, or thought, its interpretant, the thing for which it stands, its object.” (CP 1.564)

Peirce’s Semiosis and Triadomany

A core of Peirce’s world view is thus based in semiotics, the study and logic of signs. In a seminal writing, “What is in a Sign?” [6], Peirce wrote that “every intellectual operation involves a triad of symbols” and “all reasoning is an interpretation of signs of some kind.” This basic triad representation has been used in many contexts, with various replacements or terms at the nodes. One basic form is known as the Meaning Triangle, popularized by Ogden and Richards in 1923 [7], surely reflective of Peirce’s ideas.

For Peirce, the appearance of a sign starts with the representamen, which is the trigger for a mental image (by the interpretant) of the object. The object is the referent of the representamen sign. None of the possible bilateral (or dyadic) relations of these three elements, even combined, can produce this unique triadic perspective. A sign can not be decomposed into something more primitive while retaining its meaning.

Sign (Semiosis) Triad
Figure 1: The Object-Representamen-Interpretant Sign Process (Semiosis)

Let’s summarize the interaction of these three sign components [8]. The object is the actual thing. It is what it is. Then, we have the way that thing is conveyed or represented, the representamen, which is an icon, index or symbol. Then we have how an agent or the perceiver of the sign understands and interprets the sign, the interpretant, which in its barest form is a sign’s meaning, implication, or ramification. For a sign to be effective, it must represent an object in such a way that it is understood and used again. Basic signs can be building blocks for still more complex signs, such as words combined into sentences. This makes the assignment and use of signs a community process of understanding and acceptance [9], as well as a truth-verifying exercise of testing and confirming accepted associations (such as the meanings of words or symbols).

Complete truth is the limit where the understanding of the object by the interpretant via the sign is precise and accurate. Since this limit is never achieved, sign-making and understanding is a continuous endeavor. The overall process of testing and refining signs so as to bring understanding to a more accurate understanding is what Peirce meant by semiosis. Peirce’s logic of signs in fact is a taxonomy of sign relations, in which signs get reified and expanded via still further signs, ultimately leading to communication, understanding and an approximation of canonical truth. Peirce saw the scientific method as an exemplar of this process.

The understanding of the sign is subject to the contexts for the object and agent and the capabilities of the interpreting agent; that makes the interpretant an integral component of the sign. Two different interpretants can derive different meanings from the same representation, and a given object may be represented by different tokens. When the interpretant is a human and the signs are language, shared understandings arise from the meanings given to language by the community, which can then test and add to the truth statements regarding the object and its signs, including the usefulness of those signs. Again, these are drivers to Peirce’s semiotic process.

In the same early 1867 paper in which Peirce laid out the three modes of denotation of icon, index, and symbol [10] [11], he also presented his three phenomenological categories for the first time, what I (and others) have come to call his universal categories of Firstness, Secondness and Thirdness. This seminal paper also provides the contextual embedding of these categories, which is worth repeating in full:

“The five conceptions thus obtained, for reasons which will be sufficiently obvious, may be termed categories. That is,

    BEING,

Quality (reference to a ground),

Relation (reference to a correlate),

Representation (reference to an interpretant),

    SUBSTANCE.

The three intermediate conceptions may be termed accidents.” (EP 1:6, CP 1.55)

Note the commas, suggesting the order, and the period, in the listing. In his later writings, Peirce ceases to discuss Being and Substance directly, instead focusing on the ‘accidental’ categories that became the first expression of his universal categories. Being, however, represents all that there is and is the absolute, most abstract starting point for Peirce’s epistemology. The three ‘accidental’ categories of Quality, Relation and Representation are one of the first expressions of Peirce’s universal categories or Firstness, Secondness and Thirdness as applied to Substance. “Thus substance and being are the beginning and end of all conception. Substance is inapplicable to a predicate, and being is equally so to a subject.” (CP 1.548)

These two, early triadic relations — one, the denotations in signs, and, two, the universal categories — are examples of Peirce’s lifelong fascination with trichotomies [12]. He used triadic thinking in dozens of areas in his various investigations, often in a recursive manner (threes of threes). It is not surprising, then, that Peirce also applied this mindset to the general characterization of signs themselves.

Peirce returned to the idea of sign typologies and notations at the time of his Lowell Institute lectures at Harvard in 1903 [13]. Besides the denotations of icons, indexes and symbols, that he retained, and represent the three different ways to denote an object, Peirce also proffered three ways to describe the signs themselves (representamen) to fulfill different purposes, and three ways to interpret signs (interpretant) based on possibility, fact, or reason. This more refined view of three trichotomies should theoretically result in 27 different sign possibilities (3 x 3 x 3), except the nature of the monadic, dyadic and triadic relationships embedded in these trichotomies only logically leads to 10 variants (1 + 3 + 6) [14].

Peirce split the purposes (uses) of signs into qualisigns (also called tones, potisigns, or marks), which are signs that consists in a quality of feeling or possibility, and are in Firstness; into sinsigns (also called tokens or actisigns), which consist in action/reaction or actual single occurrences or facts, and are in Secondness; or legisigns (also called types or famisigns), which are signs that consist of generals or representational relations, and are in Thirdness. Instances (tokens) of legisigns are replicas, and thus are a sinsign. All symbols are legisigns. Synonyms, for example, are replicas of the same legisign, since they mean the same thing, but are different sinsigns.

Peirce split the interpretation of signs into three categories. A rheme (also called sumisign or seme) is a sign that stands for its object for some purpose, expressed as a character or a mark. Terms are rhemes, but they also may be icons or indexes. Rhemes may be diagrams, proper nouns or common nouns. A proposition expressed with its subject as a blank (unspecified) is also a rheme. A dicisign (also called dicent sign or pheme ) is the second type of sign, that of actual existence. Icons can not be dicisigns. Dicisigns may be either indexes or symbols, and provide indicators or pointers to the object. Standard propositions or assertions are dicisigns. And an argument (also called suadisign or delome) is the third type of sign that stands for the object as a generality, as a law or habit. A sign itself is an argument, including major and minor premises and conclusions. Combinations of assertions or statements, such as novels or works of art, are arguments.

Table 1 summarizes these 10 sign types and provides some examples of how to understand them:

Sign by useRelative
to
object
Relative
to
interpretant
Sign name (redundancies)Some examples
IQualisignIconRheme(Rhematic Iconic) QualisignA feeling of “red”
IISinsignIconRheme(Rhematic) Iconic SinsignAn individual diagram
IIIIndexRhemeRhematic Indexical SinsignA spontaneous cry
IVDicisignDicent (Indexical) SinsignA weathercock or photograph
VLegisignIconRheme(Rhematic) Iconic LegisignA diagram, apart from its factual individuality
VIIndexRhemeRhematic Indexical LegisignA demonstrative pronoun
VIIDicisignDicent Indexical LegisignA street cry (identifying the individual by tone, theme)
VIIISymbolRhemeRhematic Symbol (Legisign)A common noun
IXDicisignDicent Symbol (Legisign)A proposition (in the conventional sense)
XArgumentArgument (Symbolic Legisign)A syllogism

Table 1: Ten Classifications of Signs [15]

This schema is the last one fully developed by Peirce. However, in his last years, he also developed 28-class and 66-class sign typologies, though incomplete in important ways and details. These expansions reflected sign elaborations for various sub-classes of Peirce’s more mature trichotomies, such as for the immediate and dynamic objects previously discussed (see CP 8.342-379). There is a symmetry and recursive beauty to these incomplete efforts, with sufficient methodology suggested to enable informed speculations as to where Peirce may have been heading [16] [17] [18] [19].

We have taken a different path with KBpedia. Rather than engage in archeology, we have chosen to try to fathom and plumb Peirce’s mindset, and then apply that mindset to the modern challenge of knowledge representation. Peirce’s explication of the centrality and power of signs, his fierce belief in logic and reality, and his commitment to discover the fundamental roots of episteme, have convinced us there is a way to think about Peirce’s insights into knowledge representation attuned to today. Peirce’s triadomany [12], especially as expressed through the universal categories, provides this insight.


[2] Charles S. Peirce (1839 – 1914), pronounced “purse,” was an American logician, scientist, mathematician, and philosopher of the first rank. Peirce is a major guiding influence for our KBpedia knowledge system. Quotes in the article are mostly from the electronic edition of The Collected Papers of Charles Sanders Peirce, reproducing Vols. I-VI, Charles Hartshorne and Paul Weiss, eds., 1931-1935, Harvard University Press, Cambridge, Mass., and Arthur W. Burks, ed., 1958, Vols. VII-VIII, Harvard University Press, Cambridge, Mass. The citation scheme is volume number using Arabic numerals followed by section number from the collected papers, shown as, for example, CP 1.208.
[3] Some material in this article was drawn from my prior articles at the AI3:::Adaptive Information blog: “Give Me a Sign: What Do Things Mean on the Semantic Web?” (Jan 2012); “A Foundational Mindset: Firstness, Secondness, Thirdness” (March 2016); “The Irreducible Truth of Threes” (Sep 2016); “Being Informed by Peirce” (Feb 2017). For all of my articles about Peirce, see http://www.mkbergman.com/category/c-s-peirce/.
[4] Peirce actually spelled it “semeiosis”. While it is true that other philosophers such as Ferdinand de Saussure also employed the shorter term “semiosis”, I also use this more common term due to greater familiarity.
[5] The URI “sign” is best seen as an index: the URI is a pointer to a representation of some form, be it electronic or otherwise. This representation bears a relation to the actual thing that this referent represents, as is true for all triadic sign relationships. However, in some contexts, again in keeping with additional signs interpreting signs in other roles, the URI “sign” may also play the role of a symbolic “name” or even as a signal that the resource can be downloaded or accessed in electronic form. In other words, by virtue of the conventions that we choose to assign to our signs, we can supply additional information that augments our understanding of what the URI is, what it means, and how it is accessed.
[6] Charles Sanders Peirce. 1894. “What is in a Sign?”. Retrieved from http://www.iupui.edu/.
[7] C.K. Ogden and I. A. Richards. 1923. The Meaning of Meaning. Harcourt, Brace, and World, New York.
[8] Peirce himself sometimes used a Y-shaped figure. The triangle is simpler to draw and in keeping with the familiar Ogden and Richards figure of 1923.
[9] Catherine Legg. 2010. “Pragmaticism on the Semantic Web”. In Ideas in Action: Proceedings of the Applying Peirce Conference, 173–188. Retrieved from http://www.nordprag.org/nsp/1/Legg.pdf.
[10] Charles S. Peirce. 1867. “On a New List of Categories”. In Proceedings of the American Academy of Arts and Sciences.
[11] Among all of his writings, Peirce said “The truth is that my paper of 1867 was perhaps the least unsatisfactory, from a logical point of view, that I ever succeeded in producing; and for a long time most of the modifications I attempted of it only led me further wrong.” (CP 2.340).
[12] See CP 1.568, wherein Peirce provides “The author’s response to the anticipated suspicion that he attaches a superstitious or fanciful importance to the number three, and forces divisions to a Procrustean bed of trichotomy.”
[13] Charles S. Peirce and The Peirce Edition Project. 1998. “Nomenclature and Divisions of Triadic Relations, as Far as They Are Determined”. In The Essential Peirce: Selected Philosophical Writings, Volume 2 (1893-1913). Indiana University Press, Bloomington, Indiana, 289–299.
[14] Understand each trichotomy is comprised of three elements, A, B and C. The monadic relations are a singleton, A, which can only match with itself and A variants. The dyadic relations can only be between A and B and derivatives. And the triadic relations are between all variants and derivatives. Thus, the ten logical combinations for the three trichotomies are: A-A’-A’’; B-A’-A’’; B-B’-A’’; B-B’-B’’; C-A’-A’’; C-B’-A’’; C-B’-B’’; C-C’-A’’; C-C’-B’’; and C-C’-C’’, for a total of ten options.
[15] From CP 2.254-263, EP 2:294-296, and MS 540 of 1903.
[16] Priscila Borges. 2010. “A Visual Model of Peirce’s 66 Classes of Signs Unravels His Late Proposal of Enlarging Semiotic Theory”. . 221–237. https://doi.org/10.1007/978-3-642-15223-8_12.
[17] Robert W. Burch. 2011. “Peirce’s 10, 28, and 66 Sign-Types: The Simplest Mathematics”. Semiotica 2011, 184. https://doi.org/10.1515/semi.2011.023.
[18] P. Farias and J. Queiroz. 2003. “On Diagrams for Peirce’s 10, 28, and 66 Classes of Signs”. Semiotica 147, 1/4: 165–184.
[19] Tony Jappy. 2017. Peirce’s Twenty-Eight Classes of Signs and the Philosophy of Representation: Rhetoric, Interpretation and Hexadic Semiosis. Bloomsbury Academic. Retrieved September 29, 2017 from http://www.oapen.org/search?identifier=625766.
Posted:November 14, 2017

KBpediaSome Basic Use Cases from KBpedia

The human propensity to categorize is based on trying to make sense of the world. The act of categorization is based on how to group things together and how to relate those things and groups to one another. Categorization demands that we characterize or describe the things of the world using what we have termed attributes in order to find similarities [1]. Categorization may also be based on the relationships of things to external things [2]. No matter the method, the results of these categorizations tend to be hierarchical, reflective of what we see in the natural world. We see hierarchies in Nature based on bigger and more complex things being comprised of simpler things, based on fractals or cellular automata, or based on the evolutionary relationships of lifeforms. According to Annila and Kuismanen, “various evolutionary processes naturally emerge with hierarchical organization” [3]. Hierarchy, and its intimate relationship with categorization and categories, is thus fundamental to the why and how we can represent knowledge for computable means.

Depending on context, we can establish hierarchical relationships between types, classes or sets, with instances or individuals, with characteristics of those individuals, and between all of these concepts. There is potentially different terminology depending on context, and the terminology or syntax may also carry formal understanding of how we can process and compute these relationships. Nillson provides a general overview of these kinds of considerations with a useful set of references [4].

Types of Hierarchical Relationships

As early as 1997 Doyle noted in the first comprehensive study of KR languages, “Hierarchy is an important concept. It allows economy of description, economy of storage and manipulation of descriptions, economy of recognition, efficient planning strategies, and modularity in design.” He also noted that “hierarchy forms the backbone in many existing representation languages” [5].

The basic idea of a hierarchy is that some item (‘thing’) is subsidiary to another item. Categorization, expressed both through the categories themselves and the process of how one splits and grows categories, is a constant theme in knowledge representation. The idea of hierarchy is central to what is treated as a category or other such groupings and how those categories or groupings are tied together. A hierarchical relationship is shown diagrammatically in Figure 1 with A or B, the ‘things’, shown as nodes.

Direct Hierarchy

Figure 1: Direct Hierarchy

All this diagram is really saying is that A has some form of superior or superordinate relationship to B (or vice versa, that B is subordinate to A). This is a direct hierarchical relationship, but one of unknown character. Hierarchies can also relate more than two items:

Simple Hierarchy

Figure 2: Simple Hierarchy

In this case, the labels of the items may seem to indicate the hierarchical relationship, but relying on labels is wrong. For example, let’s take this relationship, where our intent is to show the mixed nature of primary and secondary colors [6]:

Multi-hierarchy

Figure 3: Multiple Hierarchy

Yet perhaps our intent was rather to provide a category for all colors to be lumped together, as instances of the concept ‘color’ shows here:

Extensional Hierarchy

Figure 4: Extensional Hierarchy

The point is not to focus on colors – which are, apparently, more complicated to model than first blush – but to understand that hierarchical relations are of many types and what one chooses about a relation carries with it logical implications, the logic determined by the semantics of the representation language chosen and how we represent it. For this clarity we need to explicitly define the nature of the hierarchical relationship. Here are some (vernacular) examples one might encounter:

A

subsumes

B

A

is more basic than

B

A

is a superClassOf

B

A

is more fundamental than

B

A

is broader than

B

A

includes

B

A

is more general

B

B

is-a

A

A

is parent of

B

A

has member

B

A

has an instance of

B

A

has attribute

B

A

has part

B

Table 1: Example Hierarchical Relationships

Again, though we have now labeled the relationships, which in a graph representation are the edges between the nodes, it is still unclear the populations to which these relations may apply and what their exact semantic relationships may be.

Table 2 shows the basic hierarchical relations that one might want to model, and whether the item resides in the universal categories of Charles Sanders Peirce of Firstness, Secondness or Thirdness, introduced in one of my previous articles [7]:

Firstness

Secondness

Thirdness

attribute

token (instance)

sibling

|

sibling

child

parent

|

parent

token

type

part

whole

|

whole

sub

super

|

sub

Table 2: Possible Pairwise (―) Hierarchical Relationships

Note that, depending on context, some of the items may reside in either Secondness or Thirdness (depending on whether the referent is a particular instance or a general). Also note the familial relationships shown: child-parent-grandparent and child-child relationships occur in actual families and as a way of talking about inheritance or relatedness relations. The idea of type or is-a is another prominent one in ontologies and knowledge graphs. Natural classes or kinds, for example, fall into the type-token relationship. Also note that mereological relationships, such as part-whole, may also leave open ambiguities. We also see certain pairs, such a sub-super, child-parent, or part-whole, need context to resolve the universal category relation.

Reliance on item labels alone for the edges and nodes, even for something as seemingly straightforward as color or pairwise relationships, does not give us sufficient information to determine how to evaluate the relationship nor how to properly organize. We thus see in knowledge representation that we need to express our relationships explicitly. Labels are merely assigned names that, alone, do not specify the logic to be applied, what populations are affected, or even the exact nature of the relationship. Without these basics, our knowledge graphs can not be computable. Yet well over 95% of the assignments in contemporary knowledge bases have this item-item character. We need interpretable relationships to describe the things that populate our domains of inquiry so as to categorize that world into bite-sized chunks.

Salthe categorizes hierarchies into two types: compositional hierarchies and subsumption hierarchies [8]. Mereological and part-whole hierarchies are compositional, as are entity-attribute. Subsumption hierarchies are ones of broader than, familial, or evolutionary. Cottam et al. believe hierarchies to be so basically important as to propose a model abstraction over all hierarchical types, including levels of abstraction [9]. These discussions of structure and organization are helpful to understand the epistemological bases underlying various kinds of hierarchy. We should also not neglect recursive hierarchies, such as fractals or cellular automata, which are also simple, repeated structures commonly found in Nature. Fortunately, Peirce’s universal categories provide a powerful and consistent basis for us to characterize these variations. When paired with logic and KR languages and “cutting Nature at its joints” [10], we end up with an expressive grammar for capturing all kinds of internal and external relations to other things.

So far we have learned that most relationships in contemporary knowledge bases are of a noun-noun or noun-adjective nature, which I have loosely lumped together as hierarchical relationships. These relationships span from attributes to instances (individuals) and classes [11] or types, with and between one another. We have further seen that labels either for the subjects (nodes) or for their relationships (edges) are an insufficient basis for computers (or us!) to reason over. We need to ground our relationships in specific semantics and logics in order for them to be unambiguous to reasoning machines.

Structures Arising from Hierarchies

Structure needs to be a tangible part of thinking about a new KR installation, since many analytic choices need to be supported by the knowledge artifact. Different kinds of structure are best for different tools or kinds of analysis. The types of relations chosen for the artifact affects its structural aspects. These structures can be as simple and small as a few members in a list, to the entire knowledge graph fully linked to its internal and external knowledge sources. Here are some of the prominent types of structures that may arise from connectedness and characterization hierarchies:

  • Lists — unordered members or instances, with or without gaps or duplicates, useful for bulk assignment purposes. Lists generally occur through a direct relation assignment (e.g., rdf:Bag)
  • Neural networks (graphs) — graph designs based on connections modeled on biological neurons, still in the earliest stages with respect to relations and KR formalisms [12]
  • Ontologies (graphs) — sometimes ontologies are treated as synonymous with knowledge graphs, but more often as a superset that may allow more control and semantic representation [13] Ontologies are a central design feature of KBpedia [14]
  • Parts-of-speech — a properly designed ontology has the potential to organize the vocabulary of the KR language itself into corresponding parts-of-speech, which greatly aids natural language processing
  • Sequences — ordered members or instances, with or without gaps or duplicates, useful for bulk assignment purposes. Sequences generally occur through a direct relation assignment (e.g., rdf:Seq)
  • Taxonomies (trees)— trees are subsumption hierarchies with single (instances may be assigned to only one class) or multiple (instances may be assigned to multiple classes or types) inheritance. The latter is the common scaffolding for most knowledge graphs
  • Typologies — are essentially multi-inheritance taxonomies, with the hierarchical organization of types as natural as possible. Natural types (classes or kinds) enable the greatest number of disjoint assertions to be made, leading to efficient processing and modular design. Typologies are a central design feature of KBpedia; see further [15].

Typically KR formalisms and their internal ontologies (taxonomy or graph structures) have a starting node or root, often called ‘thing’, ‘entity’ or the like. Close inspection of the choice of root may offer important insights. ‘Entity’, for example, is not compatible with a Peircean interpretation, since all entities are within Secondness.

KBpedia’s foundational structure is the subsumption hierarchy shown in the KBpedia Knowledge Ontology (KKO) — that is, KBpedia’s upper ontology — and its nodes derived from the universal categories. The terminal, or leaf, nodes in KKO each tie into typologies. All of the typologies are themselves composed of types, which are the hierarchical classification of natural kinds of instances as determined by shared attributes (though not necessarily the same values for those attributes). Most of the types in KBpedia are composed of entities, but attributes and relations also have aggregations of types.

Of course, choice of a KR formalism and what structures it allows must serve many purposes. Knowledge extension and maintenance, record design, querying, reasoning, graph analysis, logic and consistency tests, planning, hypothesis generation, question and answering, and subset selections for external analysis are properly the purview of the KR formalism and its knowledge graph. Yet other tasks such as machine learning, natural language processing, data wrangling, statistical and probabalistic analysis, search indexes, and other data- and algorithm-intensive applications are often best supported by dedicated external applications. The structures to support these kinds of applications, or the ability to export them, must be built into the KR installation, with explicit consideration for the data forms and streams useful to possible third-party applications.


[1] The most common analogous terms to attributes are properties or characteristics; in the OWL language used by KBpedia, attributes are assigned to instances (called individuals) via property (relation) declarations.
[2] The act of categorization may thus involve intrinsic factors or external relationships, with the corresponding logics being either intensional or extensional.
[3] Arto Annila and Esa Kuismanen. 2009. “Natural Hierarchy Emerges from Energy Dispersal”. Biosystems 95, 3: 227–233. https://doi.org/10.1016/j.biosystems.2008.10.008
[4] Jørgen Fischer Nilsson. 2006. “Ontological Constitutions for Classes and Properties”. In Conceptual Structures: Inspiration and Application (Lecture Notes in Computer Science), 35–53.
[5] Jon Doyle. 1977. Hierarchy in Knowledge Representations. MIT Artificial Intelligence Laboratory. Retrieved October 24, 2017 from http://dspace.mit.edu/handle/1721.1/41988
[6] The first and more standard 3-color scheme was first explicated by J W von Goethe (1749-1832). What is actually more commonly used in design is a 4-color scheme from Ewald Hering (1834-1918).
[7] Michael K. Bergman. 2016. “A Foundational Mindset: Firstness, Secondness, Thirdness”. AI3:::Adaptive Information. Retrieved September 18, 2017 from http://www.mkbergman.com/1932/a-foundational-mindset-firstness-secondness-thirdness/
[8] Stanley Salthe. 2012. Hierarchical Structures. https://doi.org/10.1007/s10516-012-9185-0<
[9] Ron Cottam, Willy Ranson, and Roger Vounckx. 2016. “Hierarchy and the Nature of Information”. Information 7, 1: 1. https://doi.org/10.3390/info7010001
[10] Plato. “Phaedrus Dialog (page 265e)”. Perseus Digital Library. Retrieved November 11, 2017 from http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0174%3Atext%3DPhaedrus%3Apage%3D265
[11] In the OWL 2 language used by KBpedia, a class is any arbitrary collection of objects. A class may contain any number of instances (called individuals) or a class may be a subclass of another. Instances and subclasses may belong to none, one or more classes. Both extension and intension may be used to assign instances to classes.
[12] Adam Santoro, David Raposo, David G. T. Barrett, Mateusz Malinowski, Razvan Pascanu, Peter Battaglia, and Timothy Lillicrap. 2017. “A Simple Neural Network Module for Relational Reasoning”. arXiv:1706.01427 [cs]. Retrieved November 1, 2017 from http://arxiv.org/abs/1706.01427
[13] RDF graphs are more akin to the first sense; OWL 2 graphs more to the latter.
[14] In the semantic Web space, “ontology” was the original term because of the interest to capture the nature or being (Greek ὄντως, or ontós) of the knowledge domain at hand. Because the word ‘ontology’ is a bit intimidating, a better variant has proven to be the knowledge graph (because all semantic ontologies take the structural form of a graph).
[15] Michael K. Bergman. 2016. “Rationales for Typology Designs in Knowledge Bases”. AI3:::Adaptive Information. Retrieved September 18, 2017 from http://www.mkbergman.com/1952/rationales-for-typology-designs-in-knowledge-bases/

Posted by AI3's author, Mike Bergman Posted on November 14, 2017 at 3:20 pm in Adaptive Information, Big Structure, KBpedia | Comments (0)
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Posted:September 20, 2017

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Charles Sanders Peirce, approx. Age 60Another Rung on the Ladder of Knowledge

I suppose, like most philosophers, that Charles Sanders Peirce (1839-1914) often engenders much passion and strongly held views. Among the prominent authors who have written about Peirce are scholars, engineers, arm-chair philosophers, charlatans, physicists, confused thinkers, pendants, academics, linguists, mathematicians, cosmologists, biosemioticians, atheists, religionists, scientists, and writers, among other disciplines and viewpoints. Peirce maintained the discovery of truth is a community exercise, yet that consensus about many aspects of his writings eludes the Peircean community [1]. The strength of Peirce’s theories, I believe, resides most in the generals that may be derived from his world view. Despite the areas of disagreement, I think that a general conclusion shared in the Peircean community is that much can be learned about the nature of the world and knowledge of it by studying Peirce.

In this article, the last in my current series of why and how I study Peirce, I discuss the methods and approach — the methodeutic in Thirdness according to Peirce — that I use to interpret his writings. I want to continue to emphasize the general in Peirce’s writings, the Thirdness, that fixes my own beliefs [2]. These beliefs, while sufficient as a basis for action and learning (or habit), are not fixed in the sense of being inviolate. Quite the contrary. I am continuing to learn about Peirce, changing my views and beliefs as evidence presents itself. This evidence comes from either studying more of Peirce’s writings directly or learning from others’ scholarship and insightful interpretation.

Belief is not truth, and what we take today to be truth is fallible. Continuity, change, growth and learning are core concepts within Peirce’s conception of Thirdness. Peirce continued to question and test his own views, leading to changing statements and interpretation in many areas across his five decades of writings. Peirce would have never seen himself as infallible, and would disdain any of those who hold him as such. So we shall not [3].

The very scheme of Peirce’s beliefs, what he rightfully termed his architectonic, is grounded in his universal categories of Firstness, Secondness, and Thirdness [4]. Each of these formative concepts is both necessary and sufficient for building all aspects of an understanding of reality, which in Secondness also gives us a basis for understanding the fictional as a contrast to that reality. All aspects of the knowable, experienced reality, what Peirce called the phaneron, can be reduced to one or more of these universal categories, in full or degenerate form [5].

Having died more than a century ago, Peirce was part of an age just on the cusp of electricity, wireless communications, the automobile, and the airplane. The discovery of relativity, atomic energy, quantum mechanics, and computers still resided mostly into the future. So how can Peirce speak to us about these modern things and knowledge? Well, at the most fundamental levels, Peirce is very much a big picture guy, seeking to understand the essences of existence and reality. By trying to grok Peirce’s mindset and methods, I believe we can address problems Peirce did not directly address himself. Because of his timeless insights, Peirce continues to provide adaptive guidance for our changing, modern world.

Why Important to Interpret Peirce

I have maintained throughout this series that Peirce is the greatest thinker ever in the realm of knowledge representation. Yet KR, as a term of art, was not a phrase used in Peirce’s time. True, Peirce wrote much on relations and representation (via his semiotic theory of signs) and provided many insights on the nature of information and knowledge, but he never used the specific phrase of “knowledge representation” [6]. Further, while he categorized the realm of science at least 20 different times (see below), and wrote on Charles Babbage and posited the use of electricity and logic gates for reasoning machines [7], he never attempted to categorize knowledge such as what we have undertaken with the KBpedia Knowledge Ontology (KKO). While I think Peirce had more than a glimmer of an idea that reasoning machines might someday be a reality, there was no need within his time to attempt to provide the specific representational framework for doing so.

Thus, the importance of studying Peirce for me has been to tease out those principles, design bases and mindsets that can apply Peircean thinking to the modern challenge of knowledge representation. This knowledge representation is like Peirce’s categorization of science or signs, but is broader still in needing to capture the nature of relations and attributes and how they become building blocks to predicates and assertions. In turn, these constructs need to be subjected to logical tests in order to provide a defensible basis for what is knowledge and truth given current information. Then, all of these representations need to be put forward in a manner (symbolic representation) that is machine readable and computable.

In reading and studying Peirce for more than a decade it has become clear that he had insights and guidance on every single aspect of this broader KR problem. The objective has been how to take these piece parts and recombine them into a coherent whole that is consistent with Peirce’s architectonic. How can Peirce’s thinking be decomposed into its most primitive assumptions in order to build up a new KR representation? As I argue in this article, the key to unlocking this challenge has been through an understanding of the universal categories and the mindset that resides behind them. In Peirce’s own term, the universal categories are the most “indecomposable” elements of his world view.

Of course, since Peirce himself never addressed the specific challenge of knowledge representation for computers, there is no guarantee that Peirce himself would endorse this current interpretation. Further, Peirce was a stickler for terminology and evolved and changed in his thinking over his long intellectual career. An appreciation of these factors is also important to do justice in posing a Peircean view of knowledge representation.

The Terminology Tarpits

Though Peirce frequently railed against nominalism, arguing instead for a realistic view of the world, he also was very attuned to names, labels and definitions. For example, he authored some 6,000 definitions of technical terms over the years for the Century Dictionary [8]. He was in constant search for the “correct” way to label his constructs. As one instance, at various times, Peirce called abductive reasoning hypothesis, abduction, presumption, and retroduction. He also called the methodeutic speculative rhetoric, general rhetoric, formal rhetoric, and objective logic. Such changing names were not uncommon with Peirce.

Because Peirce held that the understanding of a language symbol is a process of shared consensus among its community of users, he was generally loathe to use common terms for many of his constructs. Indeed, when one of his terms, pragmatism, was adopted by William James who gave it a different spin and interpretation, Peirce disavowed his earlier term and replaced it with the term pragmaticism. “So then, the writer [Peirce], finds his bantling ‘pragmatism’ so promoted, feels that it is the time to kiss his child good-by and relinquish it to its higher destiny; while to serve the precise purpose of expressing the original definition, he begs to announce the birth of the word ‘pragmaticism’, which is ugly enough to be safe from kidnappers” [9, pp 165-166].

This penchant for “ugly” terms is not uncommon with Peirce. As examples, here are some other terminology uses from Peirce’s writings:

agapismcoenoscopyinterpretantphaneroscopysemeiotic
anancasticismcyclosylegisignpragmastic definitionsinsign
apeirydicentmedisensepragmaticismspeculative rhetoric
antethicsentelechymethodeuticprecissionstecheotic
architectonicfallibilismobjective idealismqualisignsynechism
axiagasticshylozoismpercipuumrepresentamentransuasion
ceno-pythagoreanhypostatic abstractionperiphraxyretroductiontychasticism
chorisyidioscopyphaneronrhemetychism
Examples of Obscure Peirce Terminology

Changing and “ugly” terminology is but the first of the difficulties in reading and understanding Peirce. His own evolution as a thinker, plus the interpretations of those who study them, also complicate matters. I cover this topic in the next section.

But a real point about interpretation, I think, is to try to get past his sometimes off-putting terminology. Mostly what is hard to understand are terms you may be encountering for the first time. There are rewards if you can see through the newness of this terminology to get to the meat underneath.

Eras and Changing Viewpoints

Peirce was often the first to acknowledge how he changed his views, with one set of quotes from early 1908 showing how his thinking about the nature of signs had changed over the prior two or three years [10]. Yet that was but a small snapshot of the changes Peirce made to his sign theories over time, or of his acknowledgments that his views on one matter or another had changed.

In his analysis of Peirce’s 70-plus definitions of the sign, Robert Marty distinguishes between the original three correlates of the triadic relation as ‘global triadic’ and the later six-element definition as being ‘analytic triadic’ [11, in reference to 5]. Besides this first elaboration, Peirce undertook a further extensive expansion of his theory of signs after the turn of the 20th century. In a new book [12], Jappy provides an intelligent analysis of this evolution of Peirce’s sign theories, focusing on his latter 28-sign scheme, what Jappy feels to be Peirce’s most mature (but still incomplete). Thus, with respect to signs alone, we can trace an evolution or maturation of Peirce’s sign theories that went from 3 → 6 → 10 → 28 66 elaborations. The latter 28 and 66 schemes remained incompletely developed at the time of Peirce’s death.

Similarly, Peirce’s classification of the sciences also went through considerable changes. Beverly Kent conducted a thorough analysis in 1987, much based on unpublished manuscripts at the time, that documents at least 20 different classifications of the sciences from Peirce over the period of 1866 to 1903 (the last “perennial”), with minor ones in between [13]. In addition to signs and the classification of the sciences, examples abound of evolving terminology or thinking by Peirce for other topics for which he is commonly known, such as logic (deductive v inductive v abductive), pragmatism, continuity, infinitesimals, and mathematics.

Of course, it is not surprising that an active writing career, often encompassing many drafts, conducted over a half of a century, would see changes and evolution in thinking. Many scholars have looked to specific papers or events in order to understand this evolution in thinking. Max Fisch divided Peirce’s philosophy development into three periods: 1) the Cambridge period (1851-1870); 2) the cosmopolitan period (1870-1887); and 3) the Arisbe period (1887-1914) [14]. Murphey split Peirce’s development into four phases: 1) the Kantian phase (1857-1866); 2) three syllogistic figures (1867-1870); 3) the logic of relations (1879-1884); and 4) quantification and set theory (1884-1914) [15]. Brent has a different split more akin to Peirce’s external and economic fortunes [16]. Parker tends to split his analysis of Peirce into early and mature phases [17]. It is a common theme within major scholars of Peirce to note these various changes and evolutions.

Some of this analysis asserts breakpoints and real transitions in Peirce’s thinking. Others tend to see a more gradual evolution or maturation of thinking. Some of the arguments are clearly aimed at bolstering whatever particular thesis the author is putting forward. Such is the nature of scholarship, and to be expected.

For me, I take a pragmatic view of these changes. First, some of Peirce’s earliest writings, particular his 1867 “On a New List of Categories’ [18], but also mid-career ones, are amazingly insightful and thought-provoking. There is tremendous value in these earlier writings, often infused with genius. Peirce, after all, was in the prime of his powers. Sure, I can see where some points have evolved or prior assertions have changed, but Peirce is also good at flagging those areas he sees as having been important and earlier in error. I therefore tend to rely most on his later writings, when a hard life lived, maturity and experience added wisdom and perspective to his thoughts. I tend to see his later changes more as nuanced or mature, rather than fundamental breaks with prior writings. I see tremendous continuity and consistency of world view in Peirce over time.

Sure, at the level of how specific items or ideas change over time it is important to be cognizant of when a Peirce quote or writing occurred. The jumbled nature of the original Collected Papers means they need to be used with caution, since they have no chronology. Most contemporary Peirce scholars now tend to date by year the passages they quote in order to overcome this problem. I think this is good practice, and for which I am increasingly trying to adhere. Also, I tend to not like his later terminology, since I think it errs on the side of obscurity in order to be precise, which limits its understandability to a broader community. Peirce should have realized that understandability holds sway over individualized perspective. He was silly to argue with James about the term pragmatism, as James was doing so much to promote awareness of Peirce’s ideas.

The Lens of the Universal Categories

Chronologies, terminologies, or evolutions aside, still the question remains: How can one apply Peirce and his ideas to today’s challenges? What is the essence of trying to approach and solve problems by Peircean means? Is there a mindset by which we can think through contemporary problems in domains unheard of in Peirce’s time? Are there indeed timeless truths?

I think there are.

To me, slicing through all of the complexity and the noise, are Peirce’s universal categories of Firstness, Secondness and Thirdness. I find it amazing and consistent how much Peirce himself relies on the universal categories in his own thinking and analysis. There must be something at the heart of these universal categories that make them such a powerful lodestone.

The first hurdle, I think, in attempting to understand the universal categories is the absolute abstractness of the terms Firstness, Secondness and Thirdness. In this case, I believe Peirce’s terminology fussiness to be exactly what is proper. Since, ultimately, all reality, all potential, and all emergence derives from these elements, nothing other than one, two and three will do. Everything that is, may be, or could surprise us arises from these elements. This is the absolute ground. Nothing further can be decomposed from these elements, yet everything that is and is conceivable is built from these categories. I don’t mean to be or sound religious; just logical.

So, if we have such fundamental building blocks at hand, how can we begin to understand their nature, use and implications? How can we incorporate the universal categories into our own methodeutic?  How can our thinking, the ultimate Thirdness, leverage these elements?

As might be expected, Peirce tried to get at this very question through the idea of continuity, the force at the heart of Thirdness. The universal categories are not static, but dynamic. The occasional “surprising fact” alters what we think we know about reality, which causes us to re-inspect and re-categorize our world. The dynamic universal categories, faced with the unexpected chance arising in Firstness, ripple through our awareness (reality) to cause a new understanding of the state of existence (Secondness). The universal categories give us the primitive elements by which we can again categorize and generalize our new world, a factor of Thirdness. And so the cycle continues. Truth, understood to be a limit function, gets constantly exposed as all of us test and affirm these new realities.

Peirce, the logical categorizer, concerned with methods, and interested in pragmatic approaches and solutions, understood that how we categorize our constantly emerging worlds was fundamental. His pragmatic maxim helps us decide among many possible alternatives. Perhaps we can follow his natural classification guidelines, an item of keen interest to him, and one which I have previously discussed [19], as a way to better appreciate what these universal categories of Firstness, Secondness and Thirdness are and mean, as we work to categorize our emerging world anew.

One way to do that is to follow Peirce’s directive for determining a natural class by “an enumeration of tests by which the class may be recognized in any one of its members” [20]. So, as to better understand the ideas of Firstness, Secondness and Thirdness, I have assembled as many examples as I could find from Peirce’s writings of these members of the universal categories. The following table lists these 70 or so examples of Firstness, Secondness and Thirdness, the contexts in which they arose, and a citation where to find the supporting material in Peirce’s writings:

FirstnessSecondnessThirdness
Moods or Tonesfirstsecondthird[21]
Conceptions of First, Second, Thirdindependentrelativemediating[22]
The Categoriesmonadsparticularsgenerals[23]
Time“present”“past”“future”[24]
Cognition / Spacepointlinetriangle / sphere[25]
Movementpositionvelocityacceleration[26]
Modes of Beingpossibilityexistencelaw[27]
SecondsinternalexternalThirdness[28]
Thirdsmixturescomparisonsintelligibles[29]
Modalitypossibilityactualitynecessity[30]
Phenomena 1sensationsreactionsgenerals[31]
Phenomena 2qualities of phenomenaactual factslaws (and thoughts)[32]
Active Elementschancelawhabit-taking[33]
Existencechaosregularitycontinuity[34]
Continuityfeelingefforthabit[35]
Mathematicsqualityfactslaws[36]
Ceno-Pythagorean Categoriesoriginalityobsistencetransuasion[37]
Formtonetokentype[38]
Beingqualityrelationrepresentation[39]
Protoplasmsensibilitymotiongrowth[40]
Natural Selectionindividual variationheritabilityelimination of unfavored characters[41]
Modes of Evolutionabsolute chancemechanical necessitylaw of love[42]
Doctrines of Evolutiontychasticismanancasticismagapasticism[43]
Consciousness 1feelingsense of action/reactionsense of learning[44]
Consciousness 2feelingaltersensemedisense[45]
Consciousness 3immediate feelingpolar sensesynthetical consciousnes[46]
Thought 1abstractionsuggestionassociation[47]
Thought 2possibilityinformationcognition[48]
Thought 3thought-signconnectedinterpreted[49]
Synthetical Consciousnessassociation by contiguityassociation by resemblanceintelligibility[50]
Mindfeelingsreaction-sensationsconceptions[51]
Logical Mindideasideas from prior ideasideas from prior processes[52]
Experiencessimplesrecurrencescomprehensions[53]
Informationintensionsextensionscomprehensions[54]
Knowledge Representationattributesindividualstypes[55]
Characters or Predicatesinternalexternalconceptual[56]
Relationsattributesexternal relationsrepresentations[57]
Representationsignobjectinterpretant[58]
Sign-Objecticonindexsymbol[59]
Nature of Signsqualisignsinsignlegisign[60]
Kinds of Characterssingular charactersdual charactersplural characters[61]
Symbolswords (or terms)propositionsarguments[62]
Sign-Interpretant 1emotional interpretantenergetic interpretantlogical interpretant[63]
Sign-Interpretant 2rhemesdicisignsarguments[64]
Signs 1possiblesthingscollections[65]
Signs 2abstractivesconcretetivescollectives[66]
Propositionshypotheticalcategoricalrelative[67]
Logical Termsmonadsdyadstriads[68]
Assertionspossible modalityactual modalitynecessary modality[69]
Reasoningwhat is possiblewhat is actualwhat is necessary[70]
Logical Thinkingclearness of conceptionsclearness of distinctionsclearness of practical implications[71]
Logic Methodsabductionsdeductionsinductions[72]
Logicspeculative grammarlogic and classified argumentsmethods of truth-seeking[73]
Sciences of Discoverymathematicsphilosophyspecial sciences[74]
Philosophyphenomenologynormative sciencemetaphysics[75]
Normative Sciencelogicethicsaesthetics[76]
Concepts of Metaphysicsspontaneitydependencemediation[77]
Otherscomplete in itself, freedom, free, measureless variety, freshness, multiplicity, manifold of sense, peculiar, idiosyncratic, suchness, one, new, spontaneous, vivid, sui generisotherness, comparison, action, dichotomies, mutual action, will, volition, involuntary attention, shock, sense of change, here and now, compulsion, state, occurrence, negationidea of composition, continuity, moderation, comparative, reason, sympathy, intelligence, structure, regularities, conduct, representation, middle, learning, conditional[78]
C.S. Peirce’s Universal Categories in Relation to Various Topics

Though atheists and religionists alike argue Peirce’s belief or not in God, I also find this statement by him to be another powerful expression of the universal categories: “The starting-point of the universe, God the Creator, is the Absolute First; the terminus of the universe, God completely revealed, is the Absolute Second; every state of the universe at a measurable point of time is the third.” (CP 1.362)

It took me a while to realize that Firstness, Secondness, and Thirdness are not a linear sequence, nor one in time. In fact, Peirce likens Firstness to the present, Secondness to the past, and Thirdness to the future [24]. All possibilities, Firstness, reside in the absolute present, “for nothing is more occult” (CP 2.85), the instance at which they act or are acted upon or perceive such changes causes them to come into existence, or Secondness, in relation or contrast with other instances and events, because what is real is past. The continuity of these instances through space and time, the future, enables new contexts and generalities arising from what we can learn from Secondness and Firstness. Chance events in Firstness may spring “surprises” in Secondness that trigger new cognition or mediation in Thirdness, which potentially predicates a new basis for categorization, certainly in the sense of knowledge representation, my chosen frame of reference.

My thesis is that studying these assignments in relation to the various contexts is one way to internalize the mindset of the universal categories. At the most fundamental level we can see Firstness as the raw, unexpressed possibilities of the current problem set, the building blocks for the new category, if you will. Chance is the root aspect of Firstness, which means any of these possibilities may express themselves in surprising ways, perhaps causing the need for new categorization. The actual things or events of the new category, as made manifest by their interaction or contact with what also exists in the domain at hand, provide the actual instances of Secondness. And, the generalities or continuities among these instances, classed as best we can in a natural manner, provide the Thirdness of this domain. The best way to glean meaning from this table is through deep study and contemplation.

In the context of knowledge representation, we begin with these foundational aspects of the universal categories and then keep analyzing and categorizing following this mindset. I think it is evident in the table above, sometimes to multiple levels depending on context (which requires studying some of the supporting material to the table), that Peirce applied this same method. Where questions arise about which universal category to assign something, we look to Peirce and later scholars to see if prior determinations have been postulated and argued. If so, we test those assumptions and adopt or not those assignments, based on our own logical assessments. We continue this process as we get deeper and more specific in our categorizations. No matter what the assignment, each should be subject to questioning and testing by the community of users, perhaps altering those assignments as better information or better logic is applied to the assignments. This is the process that has been followed in developing the KBpedia Knowledge Ontology (KKO), the knowledge graph of some 200 concepts that provides the upper-level scaffolding for our knowledge representation efforts.

As of the date of this writing, there is NO other knowledge representation framework besides KKO that explicitly embraces Peirce’s universal categories of Firstness, Secondness and Thirdness. While many, many insights from Peirce’s writings contribute to how we approach representing knowledge in our systems, the adoption of the mindset of universal categories is by far the most important element in how we go about constructing our representations.

A Synthetic Mindset Through Peirce’s Architectonic

Unfamiliar terminology and a triadic foundation to his philosophy make Charles Peirce a difficult guide to initially follow. Further, there are many dimensions, each richly layered, to his guidance. For those who have stayed the course, Peirce has become an invaluable guide.

The overarching framework of Peirce’s philosophy — his architectonic — is grounded in his universal categories of Firstness, Secondness and Thirdness. As a scientist and logician, Peirce applied this mindset in pragmatic and testable ways. These methods, indeed the scientific method itself, further guide how and where to apply this mindset in ways that are economical and promise the most knowledge among all of the possible paths of inquiry. Peirce’s fierce realism, the belief there is reality beyond our own minds, and his insistence that this reality is subject to inquiry and the fixation of belief leading ever closer to truth, is distinctly different than the mind-body duality put forward by Descartes.

Richard Bernstein in a recent book [79], calls this viewpoint a sea change:

“Pragmatism begins with a radical critique of Cartesianism. In one fell swoop, Peirce seeks to demolish the inter-related motifs that constitute Cartesianism [mind-body duality; primacy of personal experience; doubt as a starting condition; there are incontrovertible truths to be discovered] . . . . We can view the development of pragmatism from Peirce until its recent resurgence as developing and refining this fundamental change of philosophical orientation — this sea change. A unifying theme in all the classical pragmatists as well as their successors is the development of a philosophical orientation that replaced Cartesianism (in all its varieties).” (pp 18-19)

Our real world is constantly changing, constantly unfolding. Our real world is viewed by all of us differently, based on background, predilection, perspective and context. What we think we know about the world today is subject to inquiry and new insights. New factors are constantly arising to shift what we think we know about ourselves and our place in the world.

Knowledge representation by computers that does not explicitly account for perspective, meaning, and interpretation is doomed to be wooden and unable to handle context. Such is the state of art today. We do not all need to agree on the specifics or any single interpretation of what our domains of inquiry may be. But we do need a framework that can respect and model those differences.

To sum up, how I interpret Peirce embraces three perspectives. First, given the breadth of Peirce’s insights, I try to read as much by him and about his writings by others as I can. This exposure helps set a rich milieu for my own insights, but also in interpretation and critical judgment. Second, despite my awe of Peirce’s genius, I do not treat his writings as gospel. Were he alive today, I have no doubt that the massive increase in knowledge and information since his day would cause him to alter his own viewpoints — perhaps substantially so in some areas. There is no similar reason why any of us should shy from questioning any of Peirce’s assertions. Yet, given Peirce’s immense powers of logic, one better be well prepared with evidence and sound reasoning before undertaking such a challenge.

And, third, and most fundamentally, I try to view how to represent knowledge through the lens of Peirce’s universal categories. The tasks of defining and organizing knowledge demand that we bring meaning, context and perspective to the task. Peirce stood on the shoulders of the giants before him. We can now stand on Peirce’s shoulders to mount the next rung on the ladder of knowledge. I believe Peirce’s universal categories and what they imply offer the next adaptive climb upward for knowledge representation. As Bernstein states, “Peirce opened up a new way of thinking that is still being pursued today in novel and exciting ways by all those who have taken the pragmatic turn. This is the sea change he helped initiate.” (p 52)


[1] Many of the Peirce quotations are drawn from The Collected Papers of Charles Sanders Peirce, reproducing Vols. I-VI, Charles Hartshorne and Paul Weiss, eds., 1931-1935, Harvard University Press, Cambridge, Mass., and Arthur W. Burks, ed., 1958, Vols. VII-VIII, Harvard University Press, Cambridge, Mass. The citation scheme used for these sources is commonly seen in Peirce scholarship, and is volume number using Arabic numerals followed by section number from the collected papers, shown as, for example, CP 1.208.
[2] Peirce discusses this topic in his seminal paper, Charles S. Peirce, 1877. “The Fixation of Belief,” Popular Science Monthly 12:1-15, November 1877
[3] “To be blinded by the peculiar strength of his thinking into a type of reverence that has always been common, would certainly be to violate the very spirit which animated him.” p. xv; from the editor’s introduction to Justus Buchler, ed., 1940. Philosophical Writings of Peirce, Routledge and Kegan Paul Ltd., reissued by Dover Publications, New York NY, 1955.
[4] M.K. Bergman, 2016. “A Foundational Mindset: Firstness, Secondness, Thirdness,” AI3:::Adaptive Information blog, March 21, 2016.
[5] Peirce’s original three universal categories were expanded to six by adding what he called one “degenerate” form to Secondness and two “degenerate” forms to Thirdness, increasing the original three by an additional three. See further CP 1.365-367.
[6] The exact origin of the phrase “knowledge representation” is unclear. Given its role in symbolic representations to computers, a branch of artificial intelligence, the phrase would not be expected to be used in that sense until the mid-20th century. Knowledge representation first became prominent through systems like the GPS problem-solving program (A. Newell, J.C. Shaw, and Herbert A. Simon, 1959. “Report on a General Problem-solving Program,” in Proceedings of the International Conference on Information Processing, pp. 256–264, KRL (the Knowledge Representation Language, see Daniel G. Bobrow and Terry Winograd, 1976. “An Overview of KRL, A Knowledge Representation Language,” Stanford Artificial Intelligence Laboratory Memo AIM 293, 1976), and then the KR thesis work of Ron Brachman at Harvard (1978) followed by his early technical papers and books; see especially the popular Hector J. Levesque and Ronald J. Brachman, 2004. Knowledge Representation and Reasoning. Amsterdam: Elsevier/Morgan Kaufmann. ISBN 1-55860-932-6.
[7] References to Charles Babbage may be found at CP 2.56 and CP 4.611. For electrical logical machines, see Charles S. Peirce, 1993, “Letter, Peirce to A. Marquand” dated 30 December 1886, in Kloesel, C. et al., eds., Writings of Charles S. Peirce: A Chronological Edition: Volume 5: 1884–1886. Indiana University Press: 421-422, with an image of the letter page with the circuits on p. 423.
[8] Charles S. Peirce, 1982. Writings of Charles S. Peirce: A Chronological Edition – Volume 1, 1857-1866, compiled by the editors of the Peirce Edition Project, Indiana University Press, August 1982, 736 pages,ISBN: 978-0-253-37201-7. The editors note Peirce contributed to 16,000 entries, most in mathematics and logic, with 6,000 written solely by Peirce
[9] Charles S. Peirce, “What Pragmatism Is,” The Monist, Vol. 15, No. 2 (April, 1905), pp. 161-181; see http://www.jstor.org/stable/27899577; also CP 5.414. He also expands on this general theme in Charles S. Peirce, 1906. “Prolegomena to an Apology for Pragmaticism,” The Monist, Vol. 16, No. 4 (October, 1906), pp. 492-546; see http://www.jstor.org/stable/27899680
[10] Charles S. Peirce, 1908. “The Ten Main Trichotomies of Signs,” in “Excerpts to Lady Welby”, in Charles S. Peirce, 1998. The Essential Peirce – Volume 2: Selected Philosophical Writings (1893-1913), edited by the Peirce Edition Project, Indiana University Press, June 1998, 624 pp., ISBN: 978-0-253-21190-3; also CP 8.363-365.
[11] See his very useful ‘Analysis of the 76 definitions of the sign’ http://www.iupui.edu/~arisbe/rsources/76DEFS/76defs.HTM (Accessed March 2016).
[12] Tony Jappy, 2017. Peirce’s Twenty-Eight Classes of Signs and the Philosophy of Representation: Rhetoric, Interpretation and Hexadic Semiosis, Bloombury Press, London, 2017, 225 pp. See https://oapen.org/download?type=document&docid=625766.
[13] Beverly Kent, 1987. Charles S. Peirce: Logic and the Classification of the Sciences, McGill-Queen’s University Press, Montreal, 258 pp.
[14] Max H. Fisch, “Peirce’s Arisbe: The Greek Influence in his Later Philosophy,” in Peirce, Semiotic, and Pragmatism, p. 227
[15] Murray G. Murphey, 1993. The Development of Perice’s Philosophy. Hackett Publishing Company, Inc., Indianapolis.
[16] Joseph Brent, 1998. Charles Sanders Peirce: A Life (2nd edition), Indiana University Press, Bloomington.
[17] Kelly A. Parker, 1998. The Continuity of Peirce’s Thought. Vanderbilt University Press, Nashville.
[18] Charles S. Peirce, 1867. “On a New List of Categories,” Proceedings of the American Academy of Arts and Sciences 7 (1868), 287–298. Presented, 14 May 1867. See CP 1.545-559.
[19] M.K. Bergman, 2015. “‘Natural’ Classes in the Knowledge Web,” AI3:::Adaptive Information blog, July 13, 2015.
[20] Peirce sets this forth as one of his conditions for determining a natural classification; see CP 1.224.
[21] CP 1.355; also, Cosmogenic Philosophy, EP 1.297
[22] See CP 6.32-34
[23] This exact categorization was never used directly by Peirce (or so my investigations to date suggest). However, it is clear throughout his writings that he relates monads to Firstness, ‘particulars’ and ‘particularities’ to Secondness, and ‘generals or ‘generalities’ to Thirdness. Further, these terms are understood and used in other categorization schemes, such as those by Aristotle and Kant. We also see, by this chart, that Peirce himself employs many different terms for his universal categories. We have chosen these to be the three main categories in the KBpedia Knowledge Ontology for these reasons. See further CP 1.300-338.
[24] CP 2.84-86; see also 2.146; it is NOT 1 –> 2 –> 3 present v hic et nunc ; CP 5.459-463
[25] CP 5.263
[26] CP 1.337
[27] CP 6.343-344
[28] CP 1.365
[29] CP 1.366; This is an example of what Peirce called ‘degenerate’ categories of the category. Degenerate means that it is a component of the category, but not sufficient as a concept in the 1o and 2o
[30] CP 5.454
[31] CP 1.418-420
[32] CP 5.121
[33] CP 1.409
[34] CP 1.411 and CP 1.175
[35] CP 6.201-202; also called Tritism or Synechism (or “all that there is”)
[36] CP 1.417-420
[37] CP 2.87-89; Peirce using his obscure labels in seeking exactitude
[38] CP 4.537
[39] CP 1.555 and CP 2.418; the initial categories were actually bracketed by Being and Substance (5 categories total). In CP 4.3 Peirce re-named these labels as quality, reaction and mediation. However, in that same passage he says, “How the conceptions are named makes, however, little difference.” I have chosen to retain his earlier names because they are more commonly referenced and it retains the idea of ‘representation’, more allied with the idea of knowledge representation.
[40] CP 1.393
[41] CP 1.398
[42] CP 6.302
[43] CP 6.302
[44] CP 1.378
[45] CP 7.551; thought is taken to be as equivalent to medisense
[46] EP 1.260
[47] The analysis of the labels and relations is provided in these two articles: M.K. Bergman, 2017. “KBpedia Relations, Part III: A Three-Relations Model,” AI3:::Adaptive Information blog, May 24, 2017; and M.K. Bergman, 2017. “KBpedia Relations, Part IV: The Detailed Relations Hierarchy,” AI3:::Adaptive Information blog, June 27, 2017.
[48] CP 1.537
[49] CP 5.283-284
[50] EP 1.261
[51] CP 6.18-20
[52] CP 7.348
[53] CP 7.528 cf
[54] Peirce did not explicitly list these terms, but they can be readily and logically derived from CP 2.419-421. The idea of information being a product of depth (1o, intensionality) times breadth (2o, extensionality) is quite insightful
[55] Though ‘general type’ is a common term for Thirdness in Peirce’s writings, he rarely used ‘attibute’ and preferred particulars to ‘individuals’. ‘Attributes’ and ‘individuals’ are now in modern usage, and clearly refer to 1o and 2o, respectively.We have chosen these two terms for use in the KBpedia Knowledge Ontology for these reasons.
[56] Somewhat modified from CP 5.469 cf, with external and conceptual replacements supported by the senses of the accompany text
[57] Taken from the analysis of Peirce documented in [47]; these are the terms chosen for use in terms for use in the KBpedia Knowledge Ontology
[58] CP 1.339; ‘representation’ is also called a ‘sign’
[59] CP 1.191; can also be called ‘speculative grammar’ or ‘nature of signs’; in Jappy 2017 this is called ‘Sign-Object’, Table 1.2 A Synthesis of MSS R478 and R540, 1903
[60] CP 4.537 fn 3; called simply ‘Sign’ in Jappy 2017, Table 1.2 A Synthesis of MSS R478 and R540, 1903.
[61] CP 1.370-371; can substitute ‘facts’ for ‘characters’
[62] CP 2.95, also CP 8.337; CSP also expresses ‘arguments’ as inferences or syllogisms
[63] CP 5.475-6
[64] From Jappy 2017, Table 1.2 A Synthesis of MSS R478 and R540, 1903
[65] CP 8.366, with respect to the nature of dynamical objects
[66] CP 8.366, with respect to the nature of dynamical objects
[67] CP 2.325
[68] CP 1.293
[69] CP 4.57
[70] CP 1.369
[71] CP 3.457
[72] CP 2.98; in an earlier version, I listed ‘abduction’ as a Thirdness, but I was corrected on the Peirce-L mailing list. On the other hand, abduction is at the interface between Thirdness and Firstness, since it is the source of the possibilities that need to be considered for a given category. The dynamic nature of Peirce’s semiosis is part of the sign-making and -recognition process.
[73] CP 1.191
[74] CP 1.239-242; the ‘special sciences’ include the physical (physics, chemistry, biology, astronomy, geognosy, and whatever may be like these sciences) and the psychical (psychology, linguistics, ethnology, sociology, history, etc.) sciences
[75] CP 1.280-282
[76] CP 1.281
[77] CP 3.422; also, Forms of Rhemata (singular, dual or plural)
[78] Mostly random notes teken from various Peirce writings.
[79] Richard J Bernstein, 2010. The Pragmatic Turn, Polity Press, Malden, MA. 2010.
Posted:September 13, 2017

AI3 Pulse

KBpedia, a computable knowledge structure combining six major public knowledge bases, received a minor update today to version 1.51. This release makes some minor corrections and provides updated statistics. No material changes from version 1.50 released a month ago were made.

The KBpedia knowledge structure combines six (6) public knowledge bases – Wikipedia, Wikidata, OpenCyc, GeoNames, DBpedia and UMBEL – into an integrated whole. These core KBs are supplemented with mappings to more than a score of additional leading vocabularies. The entire KBpedia structure is computable, meaning it can be reasoned over and logically sliced-and-diced to produce training sets and reference standards for machine learning and data interoperability. KBpedia greatly reduces the time and effort traditionally required for knowledge-based artificial intelligence (KBAI) tasks. KBpedia was first released in October 2016, though it has been under active development for more than six years. KBpedia is sponsored by Cognonto Corporation.

Posted by AI3's author, Mike Bergman Posted on September 13, 2017 at 1:31 pm in KBpedia, Ontologies, Pulse, Semantic Web | Comments (0)
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