=Paper=
{{Paper
|id=Vol-1126/paper2
|storemode=property
|title=A Survey of Peirce Semiotics Ontology for Artificial Intelligence and
a Nested Graphic Model for Knowledge Representation
|pdfUrl=https://ceur-ws.org/Vol-1126/paper2.pdf
|volume=Vol-1126
|dblpUrl=https://dblp.org/rec/conf/aiia/Yian13
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==A Survey of Peirce Semiotics Ontology for Artificial Intelligence and
a Nested Graphic Model for Knowledge Representation==
https://ceur-ws.org/Vol-1126/paper2.pdf
A Survey of Peirce Semiotics Ontology for Artificial Intelligence and
a Nested Graphic Model for Knowledge Representation.
Sun Yi’an
yiansun@hotmail.com
Erasmus Mundus Joint PhD of Law Science and Technology
Abstract (survey paper): In this paper I review John Sowa’s application
of semiotics ontology to AI modeling. I begin with a survey of semiotics
theory and a definition of symbol, communication and the epistemology of
semiotics in a conceptual structure. Then I turn to Sowa’s Nested Graphic
Model of knowledge representation. Semiotics is the study of signification
in the wide sense. This means that semiotics is concerned with
significations which are not verbally conveyed, such as by texts, graphics,
or other visual signs, or by symbolic logic. Thus semiotics is a systematic
science for the AI field which searches to establish general rules and
invariants. The purpose of this paper is to analyze differences of meaning,
to explore their implications for web-based metadata, and to show how the
methods of logic and ontology can be used to define, relate, and translate
signs from one vocabulary to another. Among the methods discussed in
this paper are Peirce's systems of logic, ontology, and semiotics, which are
presented in more detail in the book Knowledge Representation by Sowa
(2000).
Keyword: 1.Nested Graphic Model (NGM) 2.Peirce Semiotics 3.
knowledge representation 4.Artificial Intelligence 5. John Sowa
1 Semiotic Interpretant, Legal Concept Representation
1.1 Saussure and Pierce’s Semiotics Ontology, Semiosis Theory
Semiotics in Europe derives from the Swiss linguist Ferdinand de
Saussure.[2] He establishes a signified and signifier module of symbol
different from that of Pierce. After Saussure, the France semiotician
Roland Barthes constructed a two-semiological system and myths of the
semiotics system. From the comparison table we can see how Saussure
deal with signifier and signified in the two semiology system in the
picture. Saussure takes the signification process to be fixed, not moving
from signifier to signified in a symbol, which is very different from
Pierce’s view of symbol.
Peirce’s semiotics Saussure's semiotics
triangle theory dual layer theory
Table 1. Comparison of Semiotics ontology models.
Meanwhile, semiotics in the United States was established by Charles S.
Peirce 1839–1914). His theory was not well accepted in the beginning.
People preferred Saussure’s view of the symbol. How to think of and
interpret a symbol is represented by two models. Peirce took the triangle
diagram to explain the symbol interpretation. He called it semiosis
process, from signifier to signified. Peirce added an element of
interpretation to explain the signification and significance of meaning,
which will be a good point to epistemology and logic for our reasoning
process representation. [2]
Since significance of legal meanings became a chain of semiosis
processes, most legal semioticians discuss rules and norms for a better
concept in semantic web. The meaning of fixed stability becomes the main
issue of ontology in reasoning. A dual semiology system for explaining
connotation and denotation meanings is a way to represent knowledge
instead of pure legal information. As for developing collective wisdom for
a better mathematics module, semiotic ontology is highly related to a
mathematic foundation. Therefore, the paper will present structural to
post-structural semiotics theories in mathematics modeling, argue for a
formulization and find more clues for solving problems or new
methodologies.
2. Pierce’s Semiotics ontology of John Sowa
Peirce's research in logic, physics, mathematics, and lexicography
made him uniquely qualified to appreciate the rigors of science, the
nuances of language, and the semiotic processes that support both. John
Sowa reviews Pierce’ semiotics ontology, the ongoing efforts to construct
a new foundation for 21st-century philosophy on the basis of Peirce's
research, and its potential for revolutionizing the study of meaning in
cognitive science, especially in the fields of linguistics and artificial
intelligence. [5]
Peirce is widely regarded as the most important philosopher born in
America, and many of his followers consider him the first philosopher of
the 21st century. An easy explanation for the neglect of his philosophy in
the 20th century is that Peirce was “born before his time.” A better
approach is to ask what trends in the 20th century led to the split between
analytic and continental philosophy, and how Peirce's logic and
philosophy relate to both sides of the split.
The study of signs, called semiotics, was independently developed by the
logician and philosopher Charles Sanders Peirce and the linguist Ferdinand
de Saussure. The term comes from the Greek sêma (sign); Peirce originally
called it semeiotic, and Saussure called it semiology, but semiotics is the
most common term today. As Saussure (1916) defined it, semiology is a
field that includes all of linguistics as a special case. But Peirce (CP 2.229)
had an even broader view of that, which includes every aspect of language
and logic within the three branches of semiotics:
1. Syntax. “The first is called by Duns Scotus grammatica speculativa.
We may term it pure grammar.” Syntax is the study that relates
signs to one another.
2. Semantics. “The second is logic proper,” which “is the formal science
of the conditions of the truth of representations.” Semantics is
the study that relates signs to things in the world and patterns of
signs to corresponding patterns that occur among the things the
signs refer to.
3. Pragmatics. “The third is... pure rhetoric. Its task is to ascertain the
laws by which in every scientific intelligence one sign gives
birth to another, and especially one thought brings forth
another.” Pragmatics is the study that relates signs to the agents
who use them to refer to things in the world and to communicate
their intentions about those things to other agents who may have
similar or different intentions concerning the same or different
things.
Metalanguage, or signs of signs, consists of signs that signify something
about other signs, but what they signify depends on what relationships
those signs have to each other, to the entities they represent, and to the
agents who use those signs to communicate with other agents. Figure 1
shows the basic relationships in a meaning triangle (Ogden and Richards
1923). On the lower left is an icon that resembles a cat named Yojo. On the
right is a printed symbol that represents his name. The cloud on the top
gives an impression of the neural excitation induced by light rays bouncing
off Yojo and his surroundings. That excitation, called a concept, is the
mediator that relates the symbol to its object.
Figure 1. The meaning triangle
Following is Peirce's definition of sign: A sign, or representamen, is
something which stands to somebody for something in some respect or
capacity. It addresses somebody, that is, creates in the mind of that person
an equivalent sign, or perhaps a more developed sign. That sign which it
creates I call the interpretant of the first sign. The sign stands for
something, its object. It stands for that object, not in all respects, but in
reference to a sort of idea, which I have sometimes called the ground of the
representamen (CP 2.228).
Figure 2. Concept of representing an object by a concept
Meaning triangles can be linked side by side to represent signs of signs of
signs. On the left of Figure 3 is the triangle of Figure 1, which relates Yojo
to his name. The middle triangle relates the name Yojo to the quoted string
“Yojo”. The rightmost triangle relates that character string to its encoding
as a bit string 0x596F6A6F. In each of the three triangles, the symbol is
related to its object by a different metalevel process: naming, quoting, or
representing. At the top of each triangle, the clouds that represent the
unobservable neural excitations have been replaced by concept nodes that
serve as printable symbols of those excitations. The concept node
[Cat:Yojo] is linked by the conceptual relation node (Name) to a node for
the concept of the name [Word:”Yojo”], which is linked by the conceptual
relation node (Repr) to a node for the concept of the character string itself
[String: 'Yojo']. The resulting combination of concept and relation nodes is
an example of a conceptual graph (CG).
Figure 3. Object, name of object, symbol of name, and character string
To deal with meaning, semiotics must go beyond relationships between
signs to the relationships of signs, the world, and the agents who observe
and act upon the world. Symbols are highly evolved signs that are related
to actual objects by previously established conventions. People agree to
those conventions by relating the symbols to more primitive signs, such as
icons, which signify their objects by some structural similarity, and indices,
which signify their objects by pointing to them. All these signs can be
related to one another by linking series or even arrays of triangles.
Additional triangles could show how a name is related to the person who
assigns the name, to the reason for giving an object one name rather than
another, or to an index that points to some location where the object may
be found.
Figure 1 shows a conceptual graph that represents the same
information. [5]
Sowa illustrated the differences in notation. Consider the English
sentence, “John is going to Boston by bus,” which could be expressed in
Peirce's algebraic notation as:
ΣxΣy(Go(x) • Person(John) • City(Boston) • Bus(y) •
Agnt(x,John) • Dest(x,Boston) • Inst(x,y))
Boole treated disjunction as logical addition and conjunction as logical
multiplication. Peirce represented the existential quantifier by Σ for
repeated disjunction and the universal quantifier by Π for repeated
conjunction. Peirce began to experiment with relational graphs for
representing logic as early as 1882, but he couldn't find a convenient
representation for all the operators of his algebraic notation. In 1896,
Peirce discovered a simple convention that enabled him to represent full
FOL: an oval enclosure that negated the entire graph or sub graph inside.
He first applied this technique to his tentative graphs whose other
operators were disjunction and the universal quantifier. In 1897, however,
he switched to the dual form, the existential graphs, which consisted of the
oval enclosure added to his earlier relational graphs.
Sowa commented that, for linguistics and artificial intelligence, the
narrow focus meant that the most important questions couldn't be asked,
much less answered. The great linguist Roman Jakobson Figure, whose
career spanned most of the 20th century, countered Chomsky with the
slogan “Syntax without semantics is meaningless.” In AI, Winograd called
his first book Understanding Natural Language (1972), but he abandoned
a projected book on semantics when he realized that no existing semantic
theory could explain how anyone, human or computer, could understand
language.
2.1 Peirce's Contributions to the Study of Meaning
Peirce not only recognized context dependence, he even developed a
notation for representing it in his existential graphs: The nature of the
universe or universes of discourse (for several may be referred to in a
single assertion) in the rather unusual cases in which such precision is
required, is denoted either by using modifications of the heraldic tinctures,
marked in something like the usual manner in pale ink upon the surface, or
by scribing the graphs in colored inks.
Figure 2: Evolution of semiosis
Although Peirce's graph logic is equivalent to his algebraic notation in
expressive power, he developed an elegant set of rules of inference for the
graphs, which have attractive computational properties. Ongoing research
on graph-theoretic algorithms has demonstrated important improvements
in methods for searching and finding relevant graphs during the reasoning
processes. [7]
3. Concept in Semantic Web, graphic representation
3.1 Contexts by Peirce and McCarthy
Later on research life, Peirce invented the algebraic notation for
predicate calculus, which, with a change of symbols by Peano, became
today's most widely used notation for logic. A dozen years later, Peirce
developed a graphical notation for logic that more clearly distinguishes
contexts. [4]One of McCarthy's reasons for developing a theory of context
was his uneasiness with the proliferation of new logics for every kind of
modal, temporal, epistemic, and non-monotonic reasoning. The
ever-growing number of modes presented in AI journals and conferences
is a throwback to the scholastic logicians who went beyond Aristotle's two
modes, necessary and possible, to the modes: permissible, obligatory,
doubtful, clear, generally known, heretical, said by the ancients, or written
in Holy Scriptures. Medieval logicians spent so much time talking about
modes that they were nicknamed the modesties. Modern logicians have
axiomatized their modes and developed semantic models to support them,
but each theory includes only one or two of the many modes. McCarthy
(1977) observed, For AI purposes, we would need all the above modal
operators in the same system. This would make the semantic discussion of
the resulting modal logic extremely complex.
4. Nested Graph Models (NGM) of John Sowa
To prove that a syntactic notation for contexts is consistent, it is
necessary to define a model-theoretic semantics for it. But to show that the
model captures the intended interpretation, it is necessary to show how it
represents the entities of interest in the application domain. For
consistency, this section defines model structures called nested graph
models (NGMs), which can denote logical expressions that contain nested
contexts. Figure shows an informal example of a nested graphs model
(NGM). Every box or rectangle in figure represents an individual entity in
the domain of discourse, and every circle represents a property (monadic
predicate) or a relation (predicate or relation with two or more arguments)
that is true of the individual(s) to which it is linked. The arrows on the arcs
are synonyms for the integers used to label the arcs: for dyadic relations,
an arrow pointing toward the circle represents the integer 1, and an arrow
pointing away from the circle represents 2; relations with more than two
arcs must supplement the arrows with integers. Some boxes contain nested
graphs: they represent individuals that have parts or aspects, which are
individual entities represented by the boxes in the nested graphs model
(NGM).
Figure 3: A nested graph model (NGM) [4]
Sowa found that Peirce (1885) used model-theoretic arguments to
justify the rules of inference for his algebraic notation for predicate
calculus. For existential graphs, Peirce (1909) defined endoporeutic as an
evaluation method that is logically equivalent to Tarski's. That equivalence
was not recognized until Hilpinen (1982) showed that Peirce's
endoporeutic could be viewed as a version of game-theoretical semantics
by Hintikka (1973). Sowa (1984) used a game-theoretical method to
define the model theory for the first-order subset of conceptual graphs.
4.1 The Dynamic meaning change model NGM
Peirce had a much simpler and more realistic theory. For him, thoughts,
beliefs, and obligations are signs. The types of signs are independent of
any mind or brain, but the particular instances—or tokens as he called
them—exist in the brains of individual people, not in an undefined
accessibility relation between imaginary worlds. Those people can give
evidence of their internal signs by using external signs, such as sentences,
contracts, and handshakes. In his definition of sign, Peirce (1902)
emphasized its independence of any implementation in proteins or silicon:
[4] He defined a sign as something, A, which brings something, B, its
interpretant, into the same sort of correspondence with something, C, its
object, as that in which it itself stands to C. In this definition, Peirce makes
no more reference to anything like the human mind than his definition a
line as the place within which a particle lies during a lapse of time. Thus
we could take Pierce’s belief of dynamic or open texture reasoning of
signs. The nested graphic model is a graphic representation model of
intelligent system design by the conceptual structure and logic
representation. It’s important in the model for AI and Law when changing
the meaning of legal texts, thus Sowa’s NGM model would contribute to
the legal ontology design for dynamic open texture ontology by the
formalizing of AI and Law logic.
4. Conclusion and future.
To sum up, we know how complex nature can be. Using a simple way of
modeling knowledge representation is an essential fundamental for system
design. In this paper, by reviewing John Sowa’s utilization of Peirce’s
semiotics theory, we can see how Nested graphic models explain the
concept structure. To continue the survey and apply the model in more
fields, like AI and Law, intelligent system design will be remarkable for
how human usage symbol as machine can apply in logic.
References
[1] Charles Morris (1976): Signification and Significance: A Study of the
Relations of Signs and Values. In Thomas Sebeok, Donna Jean Umiker
(eds.) The Hague: Mouton, pp. please insert pages numbers here.
Charles Morris, Writing on the General Theory of Signs,
[2] Ferdinand de Saussure, Course in general linguistics, edited by Charles
Bally, et al. translated from the French by Wade Baskin, New York:
McGraw-Hill, 1966
[3] John Sowa, Arun K. Majumdar, Analogical reasoning, in de Moor, Lex,
Ganter, eds., Conceptual Structures for Knowledge Creation and
Communication, Proceedings of ICCS 2003, LNAI 2746,
Springer-Verlag, Berlin, 2003, pp. 16–36.
[4] John Sowa, Laws, facts, and contexts: Foundations for multimodal
reasoning, in Knowledge Contributors, edited by V. F. Hendricks, K. F.
Jørgensen, and S. A. Pedersen, Kluwer Academic Publishers, Dordrecht,
pp. 145–184.
[5] John Sowa, Peirce’s contributions to the 21st Century, in H. Schärfe, P.
Hitzler, & P. Øhrstrøm, eds., Conceptual Structures: Inspiration and
Application, LNAI 4068, Springer, Berlin, 2006, pp. 54–69.
[6] John Sowa, Peirce’s tutorial on existential graphs, Semiotica 186:1–4,
Special issue on diagrammatic reasoning and Peircean logic
representations, 345–394.
[7]Majumdar, Arun K., John F. Sowa, & Paul Tarau (forthcoming)
“Graph-based algorithms for intelligent systems,” in A. Nayak & I.
Stojmenovic, eds., Handbook of Applied Algorithms, Wiley & Sons, New
York.
[8]Ontology, metadata, and semiotics, in B. Ganter & G. W. Mineau, eds.,
Conceptual Structures: Logical, Linguistic, and Computational Issues,
Lecture Notes in AI #1867, Springer-Verlag, Berlin, 2000, pp. 55–81.
http://www.jfsowa.com/ontology/ontometa.htm
Acknowledgement
I wish to thank Prof. Pompeu Casanovas of the LAST-JD doctorate program,
Director Prof. Monica Palmirani, Prof. Antonino Rotolo, and Prof. Guido Bella for
their tremendous research advice on my work approach. This paper is part of the
research plan for my PhD on legal semiotics in AI and Law. Thanks again for the
DWAI doctoral workshop’s fruitful discussion, and especial thanks to colleagues
Alessio Antonini and Alan Perotti of Turin University Computer Science
Department.
A computer scientist, John F. Sowa spent thirty years working on research and development projects
at IBM and is a cofounder of VivoMind Research, LLC. He has a BS in mathematics from MIT, an
MA in applied mathematics from Harvard, and a PhD in computer science from the Vrije
Universiteit Brussel. He is a fellow of the American Association for Artificial Intelligence, and he
has taught courses at the IBM Systems Research Institute, universities (Binghamton Polytechnic,
and Stanford), and summer institutes (Linguistic Society of America and UQAM Cognitive Science).
With his colleagues at VivoMind, he has been developing novel methods for using logic and
ontology in systems for reasoning and language understanding. The language of conceptual graphs,
which he designed, has been adopted as one of the three principal dialects of the ISO/IEC standard
for Common Logic. See John F. Sowa website bibliography http://www.jfsowa.com/pubs/