Self-organising Logic of Structures as an Element of the Multi-layered Language Description Maciej Piasecki G4.19 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. He 1 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, y man(x) park(y) walk_in_park(x) x=z gen(z, male) whistle(z) x, y, z

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) D e  , t (truth values) D t = {0,1} –m (discourse referents – DR – metaphor of memory) D m = any infinite set – unlimited ‘amount of memory’, < M – a total order defined on D m minimal element P 0,  p  D m.(P 0 < M p  P 0 =p) Construction of compound types –(a b), where D (a b) = D b Da –(a 1  a 2 ...a n ), 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 ‘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 states operator ... P0P0 PnPn P0P0 PnPn P n+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  ( P n, X )... P0P0 PnPn P0P0 PnPn input state output state X = PiPi... Yi  XYi  X PkPk Yk  XYk  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  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 i. j. (  (i,k 1 ) ; farmer ( #(  (k 1 ), k 1 ) )  k 1 =k 2  (k 2,k 3 ) ; donkey ( #(  (k 3 ), k 3 ) )  k 3 =k 4  own ( #(  (k 1 ), k 1 ), #(  (k 3 ), k 3 ) )  k 4 =j ) –Simplified representation of the discourse i. j. (  (i,k 1 );farmer ( #(  (k 1 ), k 1 ) )  k 1 =k 2 ;  (k 2,k 3 ) ; donkey ( #(  (k 3 ), k 3 ) )  k 3 =k 4 ; own ( #(  (k 1 ), k 1 ), #(  (k 3 ), k 3 ) )  k 4 =k 5 ;  (k 5,k 6 ) ;  (  (k 6 ), male_pron, k 6, k 7 ) ;  (k 7,k 8 ) ;  (  (k 8 ), non_hum_pron, k 8, k 9 ) ; like ( #(  (k 6 ), j), #(  (k 8 ), j) )  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. i. j. (  (i,k 1 ) ;  (  (  (k 1 ), named_jan, k 1, k 2 ) ;  (k 2,k 3 ) ;  (  ) (  (k 3 ), mountain, k 3, k 4 ) ; mountain ( #(  (k 4 ), k 4 ) )  k 4 =k 5 ; climb ( #(  (k 1 ), k 1 ), #(  (k 4 ), k 4 ) )  k 5 =j ) –E.g. ||tą górę (the/this mountain)||= i. j. (  (i,k 1 );  (  ) (  (k 1 ), mountain, k 1, k 2 ) ; mountain(#(  (k 2 ), k 2 ))  k 2 =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 C a 2 ( three )( X ) N 2 ( three )( X ) D 1 ( three )( X ) three( X )

Cardinality Dependency in SLS Binary directed relations between GQs Operators of cardinality: dependency ( ‘<‘) and indepedency ( ‘:‘)  Q three <Q two Q two >Q three matrix operator modified proto-quantifiers and their dependencies configurations of collections = the possible structures of relation  Q three <Q two  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 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 (  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 ) –other readings: >, < — narrow scope three professors, :, : — independency, a kind o cumulative reading, <, < — a kind of branching quantification. intersection operator filtered verb predicate sequence of dependency operators

Examples: Simple Discourse More 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=X= X  man (D 1 (more_than_two))(X)=  set of objects atomic collection  = ||laugh|| state:

Examples: Simple Discourse More than two men laugh. They respect some young boy. (van Eijck & Nouven, 2002) Interpretation of the second sentence:  = ||respect|| ( (D 1 (exst pl ))(Z) < (D 1 (some))(Y) ) validating intersection link X=X=Y=Y= =Z  Y  young_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  ( P n, X )... P0P0 PnPn P0P0 PnPn input state output state X = PiPi... Yi  XYi  X PkPk Yk  XYk  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 (  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 – information –structure of cardinality dependencies –quantification variety – intended by the speaker  Q three <Q two Q two >Q three matrix operator modified proto-quantifiers and 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 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 /09

Variable Free, Binding Free and Structure Oriented Discourse Compositional Interpretation Thank you very much for your attention... Maciej Piasecki G4.19 Research Group Institute of Informatics Wrocław University of Technology