Conceptual Modeling in a Semiotic Perspective, lecture at University of Rome Tor Vergata, May 2015

1. Conceptual Modeling in a Semiotic
Perspective
Guido Vetere
IBM Italia, Center for Advanced Studies
CNR, Istituto di Scienze e Tecnologie della Cognizione
Centro ricerche interdisciplinare su
cognizione, linguaggio e conoscenza
dell’Università di Roma Tor Vergata
11 Maggio 2015
K Drive
Knowledge Driven
Data Exploitation
FP7 grant 286348

2. 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

3. Conceptual Models
● Data Structures
● Database Schemas
● Industry Models
● Ontologies
● WordNets

4. 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}

5. The Logic Backbone
● Description Logic
(FOL fragment)
– Concepts
– Roles
– Individuals
– Constructors
– Assertions
B⊆A,C⊆A, B∩C=∅
A
B C
{disjoint}

6. 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)

7. 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

8. 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

9. 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

10. 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

11. 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
Representamen
Expression
Signifier
Object
Referent
Interpretant
Content
Signified
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

12. 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

13. Types of Sign
Signs can be studied from many perspectives

14. 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

15. 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)

16. Linking Ontologies and Lexical
Resources: the Semiotic Approach
W3C Ontology-Lexicon Community Group,
https://www.w3.org/community/ontolex/

17. 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-Physical
Entity
Social Entity
Sense
Entity
Information
Object
Physical
Entity
Endurant
Substance
water-1
commits-to
(annotation)
Expression
noun-water has-sense
G. Vetere, A. Oltramari,
Lexicon Ontology
Interplay in Senso
Comune, LREC 2010

18. 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