Transcript Memory-Based Learning Instance-Based Learning K

Concept Lattices as Semantic Models
Yılmaz Kılıçaslan
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
2
Three Elements of Linguistic Meaning
The external world
accommodates
meanings.
Words can be
constituents of
meanings.
REALITY
WORDS
Jon Barwise
SOURCE OF STRUCTURE:
Donald Davidson
Meaning’s
natural
home is
the mind.
LINGUISTIC
MEANING
NATURAL WORLD
1. ARISTOTELIAN
REALM OF IDEAS
2. PLATONIC
MINDS
John locke
VIEWS OF REALITY:
3 NOMINALIST
NO STRUCTURE
4. CONCEPTUALIST
MIND
5. SOLIPSIST
NO REALITY
3
The Quoational Theory
A Nominalist View of Reality
Anti-realist with regard to universals
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.
Example: John believes that Venus is spherical
B(j, ̏ Venus is spherical ̋ )
Belief verbs are relations between individuals and the quotations of sentences.
4
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:
x[‘x’ has eight letters]
does not follow from
‘bachelor’ has eight letters
it is possible to quantify into belief contexts:
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.

It is a merit of possible-worlds semantics to handle quantification
into a belief context: x[B(j, ^s(x))](m)
5
Relativizing a Proposition to a Believer
A Conceptualist View of Reality
Anti-realist like nominalists
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.
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.
6
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.
7
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.
8
The Aristotelean View of Reality
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 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.
Aristotelian View
Saul Kripke
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 ...̋
9
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
10
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.
11
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.
12
Deriving a Concept Lattice from a Formal Context
EXAMPLE:
FORMAL CONTEXT:
O = {John, Fido, Tweety}
A = {animate, smart, two-legged, furry}
CONCEPT LATTICE:
animate
smart
two-legged
John
✓
✓
✓
Tweety
✓
Fido
✓
✓
✓
furry
✓
✓
animate
j, f, t
animate,smart
j, f
animate,smart,two-legged
j
animate,two-legged
j, t
animate,smart,furry
j
animate,smart,two-legged,furry
animate, furry
f, t
animate,two-legged,furry
t
13
Concept Lattices as Domain Models
A Concept Lattice for the building domain:
building
large
Gebäude
bina
business
residential or small
residential
ev
Haus
small
house
H
O
14
FCA and Situation Types
Lexical Aspect (Aktionsart)
SITUATION TYPES
S
dynamic
durative
S1
S2
S: All existing situations
S1 ⊆ S
S2 ⊆ S
S3 ⊆ S1  S3 ⊆ S2
S3
S1
Semelfactives Activities
dynamic,telic
S2
States
dynamic,durative
S4
S3
dynamic,durative,telic
S5
S4 ⊆ S1
S5 ⊆ S4  S5 ⊆ S3
S4 − S5: Achievements
S5: Accomplishments
15
FCA and Relative Tense
A Reichenbachian Account
ASSUMPTIONS ABOUT RELATIVE TENSE
Reference Time: A relation between event time
(E) and reference time (R)
Reference Time
E ≤ R: Retrospective
E ≥ R: Prospective
(E ≤ R  E ≥ R) ⇒ R = E: Progressive
E≤R
R≥R
Retrospective
Prospective
E ≤ R, E ≥ R
Progressive
16
FCA and Thematic Roles
Central Roles
Example: ̏John sent Mary Fido from Paris ̋
S-FINAL
theme
j, f, m
 John gave Fido to Mary.
 Jean a donné Fido à Marie.
 Can Meryem’e Fido’yu verdi.
actor + experiencer = agent
actee + experiencer = patient
actor,theme
theme,exp
actee, theme
j
j,m
f,m
 John gave Mary Fido.
 Jean a donné Marie Fido.
 Can Meryem’i Fido’yu verdi.
theme
actor,theme,exp
actor,actee,theme
S-INITIAL
j
per
actee,theme,exp
j, f, m
m
p,j,m
source,per
actor,theme
actee,theme
actor,actee,theme,exp
j, p
j
OBJECT
SUBJECT
Bir çocuk camı kırdı.
Çocuğu bir arı soktu.
EXPERIENCER SUBJ STIMULUS SUBJ
x like y
x fear y
y please x
y frighten
{j}
m
m
actor,actee,theme
{source,...}
goal,per
source,goal,per
Mary
* Marie
* Meryem
{goal,...}
{m}
to Mary
à Marie
Meryem’e
17
A Bilingual Concept Lattice Generator
Objects: tuples of
synset numbers and
sets of synonymous
English words.
Attributes: the words
of the hypernymic
synsets.
18
Thematic Lattice
̏ Mary is Parisian. ̋
PARTICIPANT
̏ She was in a park. ̋
LOCATIVE
̏ She escaped the park. ̋
LOCATION_IN_COGNITION
̏ She was happy. ̋
̏ Bees were flying around. ̋
COGNITIVE_OR_IN_COGNITION
IN_ACTION
̏ A bee hit her face. ̋
̏ She got stung by another. ̋
LOCATION_IN_ACTION
ACTION_IN_COGNITION
̏ She saw her house broken into. ̋
ACTION_IN_LOCATION_AND_COGNITION
19
Thematic ‘Fractalization’ - I
20
Thematic ‘Fractalization’ - II
21
Conclusion
Concept lattices can be formal and realist models
of semantic domains for both lexical and
grammatical forms of natural language.
22