self-organising logic of structures as an element of the multi-layered language description maciej...
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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
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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
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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
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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
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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
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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
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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 =
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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
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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
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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
...
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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
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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)
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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
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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 )
... ......
...
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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)
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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
,,, ,, ,,
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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
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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
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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:
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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
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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
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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
...
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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 )
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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
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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
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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
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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
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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