Self-organising Logic of Structures as an Element of the Multi-layered Language

Description

Maciej Piasecki

G4.19 Research GroupInstitute of Informatics

Wrocław University of Technologynlp.pwr.wroc.pl

Plan of the talk• Problem, goals and ideas• Self-organising Logic of Structures

and the notion of state• Representation of context dependencies• Cardinality Dependency instead of

Scope in multiple quantifiers sentences

• Compositional, linear and incremental interpretation of the discourse

• SLS-based interpretation in the MIC perspective

Assumption• Compositionality in Montagovian

sense„The meaning of a complex expression is a function of the meanings of its parts,

and the syntactic rules by which they are combined.”

(Partee & al, 1993)

• Attractive for Formal Semantics • Attractive for the applications in

Language Technology

Problem• Anaphora in Dynamic Semantics (e.g. DRT)

A man1 is walking in the park. He1 is whistling.

• Pre-semantic interpretation?Prior knowledge about anaphoric links is a necessary

condition for the proper selection of discourse referents

man(x)

park(y)

walk_in(x,y)

x, yman(x)

park(y)

walk_in_park(x)

x=zgen(z, male)

whistle(z)

x, y, z

Goals• Strictly compositional construction

of discourse representationFollowing the main lines of Dynamic Semantics.

• Elimination of the dependency of the construction process on the syntactic indexesResulting in elimination of the use of Discourse

Referent names.

• Scope-less representation of ‘multiple quantifiers’ sentences

Ideas• Main aspects of the NP meaning:

– interaction with the context (anaphora, reference, presupposition, etc.)

– quantification (including relations among quantifier)

– and descriptional content

• The aspects are independent but cooperating

• Anaphora representation on the basis of syntactic indexing is not the appropriate way to do this

Self-organising Logic of Structures• SLS

A typed logical language, where all operators are abbreviations of the expressions of the simple core sub-language of many sorted typed logic.

• Primitive types:– e (entities) De  , t (truth values) Dt = {0,1}

– m (discourse referents – DR – metaphor of memory)• Dm = any infinite set – unlimited ‘amount of memory’,• <M – a total order defined on Dm

• minimal element P0, pDm.(P0<M p P0=p)

• Construction of compound types– (a b), where D(a b) = Db

Da

– (a1a2...an), where

naa ...a 21D

n21 aaa ...DDD =

SLS – the Notion of State• State – a compound type s = ( m((mm)t)(m(et)) )

– Initial state S0 = P0, , {P0, }

– Meaning = relation on states

‘memory’:

discourse referents

the most recently activated

next

links

discourse referents to be activated or activated earlier

assignment in the state

SLS – Context Dependencies(1)

• Dynamic formulae: – Terms of the type (s(st)) – relations on states – Test or change input states – Semantic representation of sentences and discourses

• Discourse referent activation – operator of the type (s(st)) – Changes the most recently activated DR to the next

one– Assigns it some value in each of the output statesoperator

... P0 Pn ... P0 Pn Pn+1

input state one of the output states assignment of a value

SLS – Context Dependencies(2)• Reference operator

– For the given DR and ‘a class’ generates a relation on states– Finds all appropriate DRs, such that:

• They are accessible (i.e. activated) in the given state – structural condition

• And their values belong to the given class (simplified semantic subsumption) – semantic condition

– Adds a link from the given DR to each of the appropriate DRs

– In the case of at least one pair, both DRs must be assigned the same value (indeterministic interpretation of reference)

operator (Pn , X )

... P0 Pn ... P0 Pn

input stateoutput state

X = X =

Pi ...

Yi X

Pk

Yk X

...

SLS – Context Dependencies (3)• Accessibility of DRs

– In each state, the set of accessible = the set of activated– Operators of: dynamic negation (not), implication () i

disjunction (or)– Can exclude some DRs from the set of activated– Sequential merging operator (;) preserves activation of

DRs

• ‘Access operators’ returning (for the given state):– The most recently activated DR (operator )– And the operator # getting value of the given DR from

the given state– E.g. i.j.(#((i),i) man Ů i=j) represents a test on the

input state

Examples of Links Creation• Anaphora

S1[A farmer owns a donkey.] S2[He likes it.]– Simplified representation of S1

i.j.( Ż(i,k1) ; farmer(#(Ń(k1), k1)) Ů k1=k2

Ż(k2,k3) ; donkey(#(Ń(k3), k3)) Ů k3=k4

own( #(Ń(k1), k1), #(Ń(k3), k3) ) Ů k4=j)– Simplified representation of the discourse

i.j.(Ż(i,k1);farmer(#(Ń(k1), k1)) Ů k1=k2 ;Ż(k2,k3) ; donkey(#(Ń(k3), k3)) Ů k3=k4;

own( #(Ń(k1), k1), #(Ń(k3), k3)) Ů k4=k5 ; Ż(k5,k6) ; (Ń(k6), male_pron, k6, k7) ; Ż(k7,k8) ; (Ń(k8), non_hum_pron, k8, k9)

; like( #(Ń(k6), j), #(Ń(k8), j) ) Ů k7=j)

Existential presupposition• Representation

– Modifiers of the reference operator: (strict presupposition) (weak presupposition),

– Blocking the generation of the output state in case the reference operator can not create the enough number of links, respectively: exactly one / at least one,

– E.g. Jan zdobył pewną górę.Jan climbed a (certain) mountain.

i.j.(Ż(i,k1) ; ((Ń(k1), named_jan, k1, k2) ; Ż(k2,k3) ; () (Ń(k3), mountain, k3, k4) ; mountain(#(Ń(k4), k4)) Ů k4=k5 ; climb( #(Ń(k1), k1), #(Ń(k4), k4) ) Ů k5=j)

– E.g. ||tą górę (the/this mountain)||=i.j.(Ż(i,k1); () (Ń(k1), mountain, k1, k2) ; mountain(#(Ń(k2), k2))Ůk2=j )

– And in the case of jakąś górę (a mountain) no operator

Varieties of Quantification• Proto-quantifiers – functors of type ((et) ((et) t))

Producing a Generalised Quantifier (i.e. set of sets)

• Variety modifiers (following van der Does, 1994)E.g. let X=#((i),i) be the value of some DR

distributive

collective neutral Ca

2(three)(X) N2(three)(X) D1(three)(X) three( X )

... ......

...

Cardinality Dependency in SLS• Binary directed relations between GQs

Operators of cardinality: dependency (‘<‘) and indepedency (‘:‘)

Qthree<QtwoQtwo>Qthree

matrix operator

modified proto-quantifiersand their dependencies

configurations of collections = the possible structures of relation

Qthree<Qtwo

• Quantification structures in a sentence (phrase)

Representation of Simple Sentence• Verb predicates denotation

– Type ((et)i t) t), where i is a number of arguments

– A set of configurations of collectionsThe configurations correspond to some set of

eventualities

,,, ,, ,,

Truth Value of Simple Sentence = Intersection

matrix operator the set of potential configurations of collections

,,, ,, ,,

verb predicate denotation

all and only objects from the values of the given DRs

Representation of Multiple Quantifiers Sentence

e.g. Three professors marked two papers.• Semantic representation (simplified a little):

– distributive, ‘wide scope’ reading of three professors

i.j.((i,k1) ; #((k1), k1)professork1=k2 ; (k2,k3);#((k3),k3)paperk3=k4 ; 2(

2(, , marked), M2( <, >, D1(three)( #((k1),j) ) ), D1(two)( #((k3),j) ) ), #((k1),l), #((k3),j)

)  k4 = j )– other readings: >, < — narrow scope three professors,

:, : — independency, a kind o cumulative reading, <, < — a kind of branching quantification.

intersection operatorfiltered verb predicatesequence of dependency operators

Examples: Simple DiscourseMore than two men laugh. They respect some young boy.

(van Eijck & Nouven, 2002)

• Interpretation of the first sentence:

activated DR

assignment

validating intersection(‘situation’)

X=

Xman

(D1(more_than_two))(X)=

set of objects

atomic collection

= ||laugh||

state:

Examples: Simple DiscourseMore than two men laugh. They respect some young boy.

(van Eijck & Nouven, 2002)

• Interpretation of the second sentence:

= ||respect||

( (D1(exstpl))(Z) < (D1(some))(Y) )

validating intersection

link

X= Y==Z

Yyoung_boy

SLS: Semantic vs Pragmatic Aspects• SLS crosses the border between semantics

and pragmatics, e.g.– Reference operator: searches across ordered list of

discourse referents– Presupposition operators: constrain results produced

reference operator– Initial state: ordered list of discourse referents

+ assignments• SLS operators define the schemes,

not the full-fledged implementation,– E.g. neither linguistic structure nor speaker focus are

not implemented in the reference operator– SLS must be augmented with respect to the

pragmatic level

SLS in the Meta-Informative Grounding Perspective (1)

• Meta-informative structure of the state– linguistic structure – anaphora resolution– Centres of Attention – order of discourse

referents and their accessibility– knowledge structures – presupposition

accommodation

operator (Pn , X )

... P0 Pn ... P0 Pn

input stateoutput state

X = X =

Pi ...

Yi X

Pk

Yk X

...

SLS in the Meta-Informative Grounding Perspective (2)• Mapping: linear linguistic structure –

dependency structure– verb predicate – semantic interpretation

of arguments

i.j.((i,k1) ; #((k1), k1)professork1=k2 ; (k2,k3);#((k3),k3)paperk3=k4 ; 2(

2(, , marked), M2( <, >,

D1(three)( #((k1),j) ) ), D1(two)( #((k3),j) ) ), #((k1),l), #((k3),j)

)  k4 = j )

SLS in the Meta-Informative Grounding Perspective (3)

• Mapping: meta-information – information– structure of cardinality dependencies– quantification variety – intended by the

speaker

Qthree<QtwoQtwo>Qthree

matrix operator

modified proto-quantifiersand their dependencies

configurations of collections = the possible structures of relation

SLS in the Meta-Informative Grounding Perspective (4)• Assignments vs verb interpretation in

grounding– situations (configurations of collection)

represented by the verb

• Assignments vs grounding– communicative grounding

• restrictions on assignments and Centres of Attention

• meta-informative validation

– ontological grounding – contextually sensitive interpretation of predicates

Discourse Interpretation as A Problem of Constraints Satisfaction• Intra-sentential level

– The denotation of verbal predicate must satisfy the constraint introduced by the nominal parti.e. the constraints defining the set of

possible configurations of collections

• Inter-sentential level– A ‘chain’ of constraints– Linked by referential links

Conclusions• Expressions of SLS ‘look for’ binding with the

previous expressions by the virtue of their properties.

• Linking in SLS tries to mimic linking in natural language.

• SLS more manipulates structures of objects than assignments.

• The structures organise themselves from ‘inside’.• Further enrichment of the state and multi-level SLS

interpretation are required.

Work co-financed by the European Union Innovative Economy Programme project NEKST POIG.01.01.02-14- 013/09

Variable Free, Binding Free and Structure Oriented Discourse

Compositional Interpretation

Thank you very much for your attention...

Maciej PiaseckiG4.19 Research GroupInstitute of Informatics

Wrocław University of Technology