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Concept Lattices as Semantic Models

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

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Three Elements of Linguistic Meaning

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WORDS REALITY

MINDS

LINGUISTIC MEANING

Words can be constituents of meanings.

Donald Davidson

The external world accommodates meanings.

Jon Barwise

Meaning’s natural home is the mind.

John locke

VIEWS OF REALITY:

1.ARISTOTELIAN

2. PLATONIC

3 NOMINALIST

4. CONCEPTUALIST

5. SOLIPSIST

NATURAL WORLD

REALM OF IDEAS

NO STRUCTURE

MIND

NO REALITY

SOURCE OF STRUCTURE:

The Quoational TheoryA Nominalist View of Reality

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Anti-realist with regard to universals

Example: John believes that Venus is spherical

Universals do not exist.

Quotations conceived of as objects Language is subsumed by reality.

A Version of First-Order Logic

Belief verbs are relations between individuals and the quotations of sentences.

B(j, Venus is spherical )

Belief verbs are relations between individuals and the quotations of sentences.

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:

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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 sphericaland for him not to know that the Morning Star is Venus.

x[B(j, ^s(x))](m)

Relativizing a Proposition to a BelieverA Conceptualist View of Reality

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Anti-realist like nominalists

Example: John believes 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.

Universals do not exist.

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.

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.

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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.

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The Aristotelean View of Reality

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Realist View Particulars and universals exist independent of people’s minds and words.

Platonic View Particulars and universals exist in different realms and are not causally connected.

Scientific View1) 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.

Aristotelian View Universals are real but their existence is dependent on particulars.

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

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

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A mathematical theory of concepts and concept hierarchies which aims to derive a formal ontology from a collection of objects and their attributes

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

attributesand– the intent consists of all attributes shared by the given

objects.

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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.

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Deriving a Concept Lattice from a Formal Context

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O = {John, Fido, Tweety}A = {animate, smart, two-legged, furry}

EXAMPLE: FORMAL CONTEXT:animate smart two-legged furry

John ✓ ✓ ✓Tweety ✓ ✓ ✓Fido ✓ ✓ ✓

animate

j, f, t

animate,smart

j, f

animate, furry

f, t

animate,two-legged

j, t

animate,smart,two-legged

j

animate,two-legged,furry

tanimate,smart,furry

j

animate,smart,two-legged,furry

CONCEPT LATTICE:

Concept Lattices as Domain Models

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Gebäude

Haus

ev

bina

business

building

largeresidential or small

smallresidential

house

H O

A Concept Lattice for the building domain:

FCA and Situation TypesLexical Aspect (Aktionsart)

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S

dynamic,durative

S3

dynamic

S1

durative

S2

S: All existing situationsS1 ⊆ SS2 ⊆ SS3 ⊆ S1 S3 ⊆ S2

S3S1

S2

Semelfactives StatesActivitiesdynamic,telic

S4

dynamic,durative,telic

S5

S4 ⊆ S1S5 ⊆ S4 S5 ⊆ S3S4 − S5: AchievementsS5: Accomplishments

SITUATION TYPES

FCA and Relative TenseA Reichenbachian Account

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Reference Time

E ≤ R, E ≥ R

Progressive

E ≤ R

Retrospective

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

ASSUMPTIONS ABOUT RELATIVE TENSE

Prospective

R ≥ R

FCA and Thematic RolesCentral Roles

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theme

j, f, m

actor,theme

j

actee, theme

f,m

actor,actee,theme

theme,exp

j,m

actor,theme,exp

j

actor,actee,theme,exp

actee,theme,exp

m

theme

j, f, m

actor,theme

j

actee,theme

m

actor,actee,theme

per

p,j,m

source,per

j, pgoal,per

m

source,goal,per

Example: John sent Mary Fido from Paris

{j}{source,...}

{m}{goal,...} to Mary

à MarieMeryem’e

Mary* Marie* Meryem

John gave Mary Fido. Jean a donné Marie Fido. Can Meryem’i Fido’yu verdi.

John gave Fido to Mary. Jean a donné Fido à Marie. Can Meryem’e Fido’yu verdi.

SUBJECT OBJECT

S-FI

NA

LS-

INIT

IAL

actor + experiencer = agentactee + experiencer = patient

Bir çocuk camı kırdı.Çocuğu bir arı soktu.

EXPERIENCER SUBJ STIMULUS SUBJ

x like y y please xx fear y y frighten

A Bilingual Concept Lattice Generator

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Objects: tuples of synset numbers and sets of synonymous English words.Attributes: the words of the hypernymic synsets.

Thematic Lattice

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LOCATIVE COGNITIVE_OR_IN_COGNITION IN_ACTION

PARTICIPANT

ACTION_IN_LOCATION_AND_COGNITION

LOCATION_IN_COGNITION LOCATION_IN_ACTION ACTION_IN_COGNITION

Mary is Parisian.

She was in a park.

Bees were flying around.

She was happy.

A bee hit her face.

She got stung by another.

She escaped the park.

She saw her house broken into.

Thematic ‘Fractalization’ - I

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Thematic ‘Fractalization’ - II

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Conclusion

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