Selforganising Logic of Structures as an Element of

Self-organising Logic of Structures as an Element of the Multi-layered Language Description Maciej Piasecki G 4. 19 Research Group Institute of Informatics Wrocław University of Technology nlp. 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 man 1 is walking in the park. x, y man(x) park(y) walk_in(x, y) He 1 is whistling. x, y, z man(x) park(y) walk_in_park(x) x=z • Pre-semantic interpretation? gen(z, male) whistle(z) Prior knowledge about anaphoric links is a necessary condition for the proper selection of discourse referents

Goals • Strictly compositional construction of discourse representation Following the main lines of Dynamic Semantics. • Elimination of the dependency of the construction process on the syntactic indexes Resulting 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 P 0, p Dm. (P 0<M p P 0=p) • Construction of compound types – (a b), where D(a b) = Db. Da – (a 1 a 2. . . an), where =

SLS – the Notion of State • State – a compound type s = ( m ((m m)t) (m(et)) ) – Initial state S 0 = P 0, , { P 0, } – Meaning = relation on states discourse referents ‘memory’: assignment in the state the most recently activated next discourse referents to be activated or activated earlier links

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 states operator one of the output states input state P 0 . . . Pn Pn+1 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 ) input state P 0 . . . Pn X = P 0 output state . . . Pk . . . Pi . . . Pn Yk X Yi X 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. li. lj. (#( (i), i) man Ů i=j) represents a test on the input state

Examples of Links Creation • Anaphora S 1[A farmer owns a donkey. ] S 2[He likes it. ] – Simplified representation of S 1 li. lj. ( Ż(i, k 1) ; farmer(#(Ń(k 1), k 1)) Ů k 1=k 2 ; Ż(k 2, k 3) ; donkey(#(Ń(k 3), k 3)) Ů k 3=k 4 ; own( #(Ń(k 1), #(Ń(k 3), k 3) ) Ů k 4=j) – Simplified representation of the discourse li. lj. (Ż(i, k 1); farmer(#(Ń(k 1), k 1)) Ů k 1=k 2 ; Ż(k 2, k 3) ; donkey(#(Ń(k 3), k 3)) Ů k 3=k 4; own( #(Ń(k 1), #(Ń(k 3), k 3)) Ů k 4=k 5 ; Ż(k 5, k 6) ; (Ń(k 6), male_pron, k 6, k 7) ; Ż(k 7, k 8) ; (Ń(k 8), non_hum_pron, k 8, k 9) ; like( #(Ń(k 6), j), #(Ń(k 8), j) ) Ů k 7=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. li. lj. (Ż(i, k 1) ; ( ) (Ń(k 1), named_jan, k 1, k 2) ; Ż(k 2, k 3) ; ( ) (Ń(k 3), mountain, k 3, k 4) ; mountain(#(Ń(k 4), k 4)) Ů k 4=k 5 ; climb( #(Ń(k 1), #(Ń(k 4), k 4) ) Ů k 5=j) – E. g. ||tą górę (the/this mountain)||= li. lj. (Ż(i, k 1); ( ) (Ń(k 1), mountain, k 1, k 2) ; mountain(#(Ń(k 2), k 2))Ůk 2=j ) – And in the case of jakąś górę (a mountain) no operator

Varieties of Quantification • Proto-quantifiers – functors of type ((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 three( X ) . . . collective C 2(three)(X) a . . . neutral N 2(three)(X) . . . distributive D 1(three)(X) . . .

Cardinality Dependency in SLS • Binary directed relations between GQs Operators of cardinality: dependency (‘<‘) and indepedency (‘: ‘) Qthree<Qtwo • Quantification structures in a sentence (phrase) configurations of collections modified proto-quantifiers = the possible structures of relation and their dependencies matrix operator Q <Q three two Qtwo>Qthree

Representation of Simple Sentence • Verb predicates denotation – Type ((et)i t) t), where i is a number of arguments – A set of configurations of collections The 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, k 1) ; #( (k 1), k 1) professor k 1=k 2 ; (k 2, k 3); #( (k 3), k 3) paper k 3=k 4 ; 2 ( intersection operator 2( , , marked), filtered verb predicate M 2( <, >, sequence D 1(three)( #( (k 1), j) ) ), D 1(two)( #( (k 3), j) ) of dependency ), #( (k 1), l), #( (k 3), j) operators ) k 4 = j ) – other readings: >, < — narrow scope three professors, : , : — independency, a kind o cumulative reading, <, < — a kind of branching quantification.

Examples: Simple Discourse More than two men laugh. They respect some young boy. (van Eijck & Nouven, 2002) • Interpretation of the first sentence: activated DR (D 1(more_than_two))(X)= atomic collection state: assignment X= X man set of objects validating intersection (‘situation’) = ||laugh||

Examples: Simple Discourse More than two men laugh. They respect some young boy. (van Eijck & Nouven, 2002) • Interpretation of the second sentence: link X= ( (D 1(exstpl))(Z) < (D 1(some))(Y) ) =Z Y= Y young_boy = ||respect|| validating intersection

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 ) input state P 0 . . . Pn X = P 0 output state . . . Pk . . . Pi . . . Pn Yk X Yi X X =

SLS in the Meta-Informative Grounding Perspective (2) • Mapping: linear linguistic structure – dependency structure – verb predicate – semantic interpretation of arguments i. j. ( (i, k 1) ; #( (k 1), k 1) professor k 1=k 2 ; (k 2, k 3); #( (k 3), k 3) paper k 3=k 4 ; 2( , , marked), M 2( <, >, D 1(three)( #( (k 1), j) ) ), D 1(two)( #( (k 3), j) ) ), #( (k 1), l), #( (k 3), j) ) k 4 = j )

SLS in the Meta-Informative Grounding Perspective (3) • Mapping: meta-information – structure of cardinality dependencies – quantification variety – intended by the speaker configurations of collections modified proto-quantifiers = the possible structures of relation and their dependencies matrix operator Q <Q three two Qtwo>Qthree

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 part i. 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. 02 -14 - 013/09

Variable Free, Binding Free and Structure Oriented Discourse Compositional Interpretation Thank you very much for your attention. . . Maciej Piasecki G 4. 19 Research Group Institute of Informatics Wrocław University of Technology