Yılmaz Kılıçaslan

1. Concept Lattices as Semantic Models Yılmaz Kılıçaslan

2. Outline • Thematic Roles • History • Thematic Hierarchies • Generalized Thematic Roles • Formal Concept Analysis • Formal Concepts • Concept Lattices • Formal Contexts • Concept Lattices as Models of Thematic Structures • Thematic Tier • Action Tier • Experience Tier

3. Three Elements of Linguistic Meaning Words can be constituents of meanings. The external world accommodates meanings. MINDS WORDS REALITY Donald Davidson Jon Barwise LINGUISTIC MEANING SOURCE OF STRUCTURE: VIEWS OF REALITY: Meaning’s natural home is the mind. NATURAL WORLD ARISTOTELIAN REALM OF IDEAS PLATONIC 3 NOMINALIST NO STRUCTURE 4.CONCEPTUALIST MIND 5. SOLIPSIST NO REALITY John locke

4. The Quoational TheoryA Nominalist View of Reality Universals do not exist. Anti-realist with regard to universals Quotations conceived of as objects Language is subsumed by reality. A Version of First-Order Logic B(j, ̏ Venus is spherical ̋ ) Belief verbs are relations between individuals and the quotations of sentences. Example:Johnbelieves that Venus is spherical Belief verbs are relations between individuals and the quotations of sentences.

5. Problems with the Quoational Theory • Even though it seems to be sufficiently finely discriminating for belief contexts, the Quotational Theory is not free from problems. • First of all, it is not intuitive to consider the object of a belief relation to be meaning-independent. • Also, although it is not possible to quantify into quotation: it is possible to quantify into belief contexts: • It is a merit of possible-worlds semantics to handle quantification into a belief context: x[‘x’ has eight letters] does not follow from ‘bachelor’ has eight letters It is possible for john to believe that Venus is spherical and this belief can be expressed as: John believes that the Morning Star is spherical and for him not to know that the Morning Star is Venus. x[B(j, ^s(x))](m)

6. Relativizing a Proposition to a BelieverA Conceptualist View of Reality Universals do not exist. Anti-realist like nominalists Mind as the ground for predication Mind is subsumed by reality. Semantics in terms of mental states The semantics of an object of belief might be relativized to its believer. Example:Johnbelieves that Venus is spherical might come out as true while John believes that the Morning Star is spherical is false, because John’s understanding of Venus is not the same as his understanding of the Morning Star.

7. Problems with Conceptualism • Relativization to believers’ mental states seem to provide us with meanings: • fine enough to distinguish between all pairs of belief sentences, • but, not coarse enough to make an inference like the following valid: John believes that clouds are alive. Mary believes everything that John believes. ---------------------------------------------------------- Therefore, Mary believes that clouds are alive. • We have no good way to classify the ideas that expressions stand for. • The problem of external significance is simply pushed from expressions to ideas.

8. Philosophical plausibility of non-Realist Views • The non-realist views do not seem to be very plausible on philosphical grounds: • Nominalism: The world should have structure above and beyond set membership. • Conceptualism: Mind and language would not have evolved in a structureless world. • Solipsism: It is a form of madness to really believe that the world is only a projection of one’s mind.

9. The Aristotelean View of Reality Particulars and universals exist independent of people’s minds and words. Realist View Particulars and universals exist in different realms and are not causally connected. Platonic View 1) There are properties and relations between things in this world, independent of language and mind. 2) These universals play a role in the causal order. Scientific View Universals are real but their existence is dependent on particulars. Aristotelian View ̏ this table is wooden, brown, in the room, etc. It has all these properties; and it is not a thing without properties, behind them ...̋ Saul Kripke

10. Formal Concept Analysis • Problem: How to formalize an ontology where both objects (particulars) and attributes (universals) are integrated in a systematic way. • Solution: Formal Concept Analysis A mathematical theory of concepts and concept hierarchies which aims to derive a formal ontology from a collection of objects and their attributes

11. Formal Concepts • A concept in FCA is a pair consisting of a set of objects, which is the ‘extent’, and a set of attributes, which is the ‘intent’, such that: • the extent consists of all objects that share the given attributes and • the intent consists of all attributes shared by the given objects.

12. Concept Lattices • A formal ontology derived by FCA is a concept hierarchy where: • the set of all concepts is ordered by a subconcept-superconcept relation, which is a particular order relation denoted by ≤. • If (O1,A1) and (O2,A2) are concepts, the former is said to be a subconcept of the latter, i.e. (O1,A1) ≤ (O2,A2) iff: • O1⊆ O2⇔ A1 ⊇ A2. • A set ordered in this way is called a concept lattice. • A concept lattice can be drawn as a diagram in which concepts are represented by nodes interconnected by lines going down from superconcepts to subconcepts.

13. Deriving a Concept Lattice from a Formal Context EXAMPLE: FORMAL CONTEXT: • O = {John, Fido, Tweety} • A = {animate, smart, two-legged, furry} CONCEPT LATTICE: animate,two-legged animate,two-legged,furry animate, furry animate,smart,furry animate,smart animate j, t f, t j, f, t j, f animate,smart,two-legged t j j animate,smart,two-legged,furry 13

14. Concept Lattices as Domain Models A Concept Lattice for the building domain: Gebäude building bina Haus large business residential or small ev small residential house H O

15. FCA and Situation TypesLexical Aspect (Aktionsart) SITUATION TYPES S:All existing situations S1 ⊆S S2 ⊆S S3 ⊆S1 S3 ⊆S2 S3 S1 dynamic,durative dynamic dynamic,telic durative dynamic,durative,telic S2 S2 S3 S S4 S5 S1 Semelfactives Activities States S4 ⊆S1 S5 ⊆S4  S5 ⊆S3 S4 − S5: Achievements S5: Accomplishments

16. FCA and Relative TenseA Reichenbachian Account ASSUMPTIONS ABOUT RELATIVE TENSE Reference Time: A relation between event time (E) and reference time (R) E≤ R: Retrospective E ≥R: Prospective (E≤ R E≥R) ⇒ R = E: Progressive R ≥ R E≤ R, E ≥R E≤ R Retrospective Reference Time Progressive Prospective

17. FCA and Thematic RolesCentral Roles Example:̏John sent Mary Fido from Paris ̋  John gave Fidoto Mary.  Jean a donné Fido à Marie.  Can Meryem’e Fido’yu verdi. actor + experiencer = agent actee + experiencer = patient S-FINAL  John gave Mary Fido.  Jean a donné Marie Fido.  Can Meryem’i Fido’yu verdi. theme actor,theme actee, theme actor,theme theme,exp theme actor,actee,theme source,goal,per actor,actee,theme,exp actor,theme,exp actee,theme,exp actor,actee,theme actee,theme goal,per source,per per j,m j, f, m m f,m j, f, m j, p p,j,m j m {goal,...} {source,...} S-INITIAL {j} {m} j m j OBJECT SUBJECT to Mary à Marie Meryem’e Mary * Marie * Meryem Bir çocuk camı kırdı. Çocuğu bir arı soktu. EXPERIENCER SUBJ STIMULUS SUBJ x like y y please x x fear y y frighten

18. A Bilingual Concept Lattice Generator • Objects: tuples of synset numbers and sets of synonymous English words. • Attributes: the words of the hypernymic synsets.

19. Thematic Lattice ̏ Mary is Parisian. ̋ ̏ She was in a park. ̋ ̏ She was happy. ̋ ̏ Bees were flying around. ̋ LOCATION_IN_ACTION COGNITIVE_OR_IN_COGNITION LOCATION_IN_COGNITION ACTION_IN_COGNITION ACTION_IN_LOCATION_AND_COGNITION PARTICIPANT IN_ACTION LOCATIVE ̏ She escaped the park. ̋ ̏ A bee hit her face. ̋ ̏ She got stung by another. ̋ ̏ She saw her house broken into. ̋

20. Thematic ‘Fractalization’ - I

21. Thematic ‘Fractalization’ - II

22. Conclusion Concept lattices can be formal and realist models of semantic domains for both lexical and grammatical forms of natural language.