Conceptual Modeling in a Semiotic Perspective

Guido VetereIBM Italia, Center for Advanced StudiesCNR, Istituto di Scienze e Tecnologie della Cognizione

Centro ricerche interdisciplinare sucognizione, linguaggio e conoscenzadell’Università di Roma Tor Vergata11 Maggio 2015

K DriveKnowledge DrivenData ExploitationFP7 grant 286348

Summary

● Attaining cognitive capabilities is one of the main trends of modern Computer Science (and industry)

● The research follows (and integrates) different approaches, based on evidence (data) and logic (theories)

● Logic-based approaches face the problem of providing symbols with some intepretation with respect to extra-logic entities

● However, formal logic at the basis of computer science is quite agnostic with respect to how such intepretation is given

● For every logic-based system in which interpretation is not trivial (e.g. social ones), this may result in a big issue

● However, addressing this issue is a relatively new concern (K. Liu, 2009, Semiotics in Information Systems Engineering)

● This talk is an introduction to the topic and a survey of some ongoing research

Conceptual Models

● Data Structures● Database Schemas● Industry Models● Ontologies● WordNets

The Logic Backbone

● Predicate First Order Logic (FOL)– Constants

– Predicates

– Variables

– Connectives

– Quantifiers

∀ x (B ( x)→ A(x))∧(C (x )→ A( x))∧(B( x)→¬C (x ))∧(C ( x)→¬B( x))

A

B C

{disjoint}

The Logic Backbone

● Description Logic (FOL fragment) – Concepts

– Roles

– Individuals

– Constructors

– Assertions

B⊆A ,C⊆A , B∩C=∅

A

B C

{disjoint}

Logical Semantics

● Relation between expressions of a language and the objects (or states of affairs) referred to by those expressions

● A sentence (proposition) is true if and only if the corresponding state of affairs holds (Truth-schema)

– “the snow is white” iff the snow is white

Alfred Tarski, 1944 The Semantic Conception of Truth and the Foundations of Semantics

WHITE (SNOW)

Logical Semantics

● Given– A logic language of individual

constants, predicates, operators and inference rules

– A theory, i.e. a set of valid formulas true by definition (axioms)

– A model, i.e. a set of assignments of truth values to predicates with respect to individuals (interpretation), which fulfills the theory

● Infer the truth value of (well formed) logic formulas

PERSON (JHON ) , PERSON (MARY )HATES (MARY , JHON )

Δ={JHON , MARY }Α={PERSON () , LOVES ( ,) , HATES ( ,)}Λ=¬,∧ , →

∀ x , y LOVES (x , y)→ PERSON ( X )∧PERSON (Y )∀ x , y HATES (x , y)→ PERSON ( X )∧PERSON (Y )∀ x , y HATES (x , y)→¬LOVES (x , y)

LOVES (MARY , JHON )=F

Alfred Tarski, 1944 The Semantic Conception of Truth and the Foundations of Semantics

Tarskian Semantics in Information Systems

● Software Programs

– Runtime Memory = Model of data types \ structures

● Databases

– Database Instance = Model of the Schema

● Semantic Web \ Linked Open Data

– RDF Datasets = Model of some Ontology

● Knowledge Base (Graph)

– Assertional Box = Model of the Ontology

Activity={Patching ,Overlay ,Crack Sealing }

interpretation

Applicability of the Truth-schema

The problem of the definition of truth obtains a precise meaning and can be solved in a rigorous way only for those languages whose structure has been exactly specified.At the present time the only languages with a specified structure are the formalized languages of various systems of deductive logic.[..] We are able, theoretically, to develop in them various branches of science, for instance, mathematics and theoretical physics. [..] For other languages -- thus, for all natural, "spoken" languages -- the meaning of the problem is more or less vague, and its solution can have only an approximate character.

Tarski, 1944

Many conceptual models are out of the scope of the Truth-schema; typically, those dealing with linguistic concepts

Semantics for Natural Languages

● Relativity

– Different agents may supply different interpretations

● Vagueness

– Many predicates can not be always clearly intepreted

● Creativity

– Interpretations may be invented on the fly (and rapidly forgotten)

The snow is white

The bond between the signifier and the signified is arbitrary

F. De Saussure, Cours de lingui- stique generale, 1916

Semiotics

The snow is white

WHITE SNOW

● Manifest significant entities have no direct correspondence to extra-linguistic entities

● Instead, they relate to mediating entities, which in turn may relate to extra-linguistic ones

● The resulting structure is called sign

● Semiotics is an investigation about sign relationships, their nature and their interplay

RepresentamenExpressionSignifier

ObjectReferent

InterpretantContentSignified

sign

A sign [...] is something which stands to somebody for something in some respect or capacity. The sign stands for [...] its object [..] in reference to a sort of idea

C.S. Peirce, Collected Papers, 1897

Meaning Theories for Natural Language

● Correspondence– Aristotelism, logical positivism, L. Wittgenstein (Tractatus Logico-Philosophicus, 1921)– Speakers and listeners can verify truth conditions for sentences (T-scheme)– There’s a common access to a common World– Ontologies are given for everybody (realism)

● Interpretation– D. Davidson (Inquiries into Truth and Interpretation, 2001), H. Putnam (Mind, Language and Reality,

1975)– Listeners ascribe speakers consistent beliefs and honest communication intentions (principle of

charity)– Listeners make hypotheses about speakers’ meaning intentions based on their own ontologies– Ontologies (conditions in the World) allow verifying interpretation hypotheses (externalism)

● Interplay– L. Wittgenstein (Philosophical Investigations, 1953), D.K. Lewis (Philosophical Papers I, 1983)– Listeners and speakers share linguistic rules by virtue of social exchanges (e.g. feedbacks)– Listeners understand speakers by making explicit reasoning on these rules – Ontologies are shared as long as they work within social linguistic environments (intersubjectivity,

constructivism)● Translation

– W.V.O. Quine (Word and Object, 1960)– Speakers’ ontological commitments are not accessible by listeners– Listeners assign meanings to expressions on the basis of speakers’ observable behaviors– There are no shared ontologies (relativism)

Reality

Subjectivity

Types of SignSigns can be studied from many perspectives

Types of Concepts

N. Guarino et al, An Ontology of Meta-Level Categories, KR 94

● Model-theoretic semantics: interpretation is not in question

● Still, it is possible to spot “interpretation-critical” areas

Formal ontology focuses on different types of concepts

Vagueness Meta-Ontology

P. Alexopoulos et al (2014), “A Metaontology for Annotating Ontology Entities with Vagueness Descriptions”, Springer. 2014.

Vagueness is explicitely dealt with in recent proposals(FP7 K Drive Poject)

Linking Ontologies and Lexical Resources: the Semiotic Approach

W3C Ontology-Lexicon Community Group, https://www.w3.org/community/ontolex/

Lexicon Ontology Interplay in Senso Comune

If the sense S maps to the concept C, then there are entities of type C to which occurrences of S may refer to (ontological commitment)

Non-PhysicalEntity

Social Entity

Sense

Entity

InformationObject

PhysicalEntity

Endurant

Substance

water-1

commits-to(annotation)

Expression

noun-water has-sense

G. Vetere, A. Oltramari, Lexicon Ontology Interplay in Senso Comune, LREC 2010

Conclusion

● Model-theoretic semantics of Logic and Formal Ontology delegates interpretation to “material” disciplines (e.g. Physics)

● Logic-based conceptual models in Computer Science make extensive use of concepts whose interpretation is in question (e.g. linguistic ones)

● As a result, interpretation is usually left to ad-hoc, opaque implementations

● Research is ongoing to provide more formal, transparent and systematic approaches

● Semiotics, as the “science of interpretation”, should be regarded to as the theoretical foundation of such development