An extension of DRT Some Analyses Semantics and Pragmatics of NLP Segmented Discourse Representation Theory Alex Lascarides School of Informatics University of Edinburgh university-logo Alex Lascarides SPNLP: SDRT
An extension of DRT Some Analyses Outline Present an extension of DRT with rhetorical relations 1 Logic for representing discourse semantics Logic for constructing logical forms Apply SDRT to some semantics tasks 2 university-logo Alex Lascarides SPNLP: SDRT
An extension of DRT rhetorical relations Some Analyses Constructing logical form Claims Rhetorical relations are an essential component of 1 discourse semantics Constructing logical form doesn’t involve full access to the 2 logic for interpreting logical form. (1) a. There are unsolvable problems in number theory. b. Any even number greater than two is equal to the sum of two primes, for instance. In fact, constructing logical form has only partial access to: 3 Lexical semantics, domain knowledge, cognitive states etc. for similar reasons. university-logo Alex Lascarides SPNLP: SDRT
An extension of DRT rhetorical relations Some Analyses Constructing logical form Need Rhetorical Relations: Some Motivating Data Pronouns (2) a. John had a great evening last night. b. He had a fantastic meal. c. He ate salmon. d. He devoured lots of cheese. e. He won a dancing competition. f. ??It was a beautiful pink. John had a lovely evening Elaboration He won a He had a great meal dancing competition Narration Elaboration university-logo He ate salmon He devoured cheese Narration Alex Lascarides SPNLP: SDRT
An extension of DRT rhetorical relations Some Analyses Constructing logical form More Motivation for Rhetorical Relations Tense (3) Max fell. John helped him up. (4) Max fell. John pushed him. (5) John hit Max on the back of his neck. Max fell. John pushed him. Max rolled over the edge of the cliff. Words (6) a. A: Did you buy the apartment? b. B: Yes, but we rented it./ No, but we rented it. Bridging (7) a. John took an engine from Avon to Dansville. university-logo b. He picked up a boxcar./He also took a boxcar. Alex Lascarides SPNLP: SDRT
An extension of DRT rhetorical relations Some Analyses Constructing logical form The Strategy SDRSs: Extend DRT with rhetorical relations. 1 L ulf : Supply a separate logic for describing SDRSs 2 (semantic underspecification). Glue logic: Construct logical form for discourse via: 3 default reasoning, over 1 L ulf -formulae for clauses which are generated by the 2 grammar and ‘shallow’ representations of lexical semantics, domain 3 knowledge, cognitive states. . . Glue logic entails more consequences about content than the grammar does. These are implicatures . university-logo Alex Lascarides SPNLP: SDRT
An extension of DRT rhetorical relations Some Analyses Constructing logical form Review of DRT f [ [ � U , ∅� ] ] M g iff dom ( g ) = dom ( f ) ∪ U 1 [ K ⊕ �∅ , γ � ] ] ◦ [ f [ ] M g iff f [ [ K ] [ γ ] ] M g 2 f [ [ R ( x 1 , · · · , x n ) ] ] M g iff f = g and � f ( x 1 ) , · · · , f ( x n ) � ∈ I M ( R ) 3 [ ¬ K ] f [ ] M g iff f = g and there’s no h such that f [ [ K ] ] M h 4 [ K ⇒ K ′ ] f [ ] M g ) iff f = g and for all h such that f [ [ K ] ] M h 5 [ K ′ ] there’s an i such that h [ ] M i . university-logo Alex Lascarides SPNLP: SDRT
An extension of DRT rhetorical relations Some Analyses Constructing logical form Logic of Information Content: Syntax SDRS-formulae: DRSs R ( π, π ′ ) , where R is a rhetorical relation and π and π ′ are labels. Boolean combinations of these An SDRS is a structure � A , F , LAST � A is a set of labels F maps labels to SDRS -formulae (i.e., labels tag content) LAST is a label (of the last utterance) Where Succ ( π, π ′ ) means R ( π ′ , π ′′ ) or R ( π ′′ , π ′ ) is a literal in F ( π ) : A forms a partial order under Succ with a unique root. university-logo Alex Lascarides SPNLP: SDRT
An extension of DRT rhetorical relations Some Analyses Constructing logical form SDRSs allow Plurality Of Relations: Contrast ( π 1 , π 2 ) , Narration ( π 1 , π 2 ) (6) a. A: Did you buy the apartment? b. B: Yes, but we rented it. Of Attachment sites: Correction ( π 2 , π 3 ) , Elaboration ( π 1 , π 3 ) (8) π 1 A: Max owns several classic cars. π 2 B: No he doesn’t. π 3 A: He owns two 1967 Alfa spiders. A single utterance can make more than one illocutionary contribution to the discourse. university-logo Alex Lascarides SPNLP: SDRT
An extension of DRT rhetorical relations Some Analyses Constructing logical form A Diagram Max owns several classic cars Correction No he doesn’t Elaboration Correction He owns two 1967 spiders university-logo Alex Lascarides SPNLP: SDRT
An extension of DRT rhetorical relations Some Analyses Constructing logical form Example (2) π 1 John had a great evening last night. π 2 He had a great meal. π 3 He ate salmon. π 4 He devoured lots of cheese. π 5 He then won a dancing competition. (2) ′ � A , F , LAST � , where: A = { π 0 , π 1 , π 2 , π 3 , π 4 , π 5 , π 6 , π 7 } F ( π 1 ) = K π 1 , F ( π 2 ) = K π 2 , F ( π 3 ) = K π 3 , F ( π 4 ) = K π 4 , F ( π 5 ) = K π 5 , F ( π 0 ) = Elaboration ( π 1 , π 6 ) F ( π 6 ) = Narration ( π 2 , π 5 ) ∧ Elaboration ( π 2 , π 7 ) F ( π 7 ) = Narration ( π 3 , π 4 ) LAST = π 5 university-logo Alex Lascarides SPNLP: SDRT
An extension of DRT rhetorical relations Some Analyses Constructing logical form Other Ways of Showing This π 0 π 1 , π 6 π 1 : K π 1 π 2 , π 5 , π 7 π 2 : K π 2 , π 5 : K π 5 Narration ( π 2 , π 5 ) π 0 : π 3 , π 4 π 6 : π 7 : π 3 : K π 3 , π 4 : K π 4 , Narration ( π 3 , π 4 ) Elaboration ( π 2 , π 7 ) Elaboration ( π 1 , π 6 ) university-logo Alex Lascarides SPNLP: SDRT
An extension of DRT rhetorical relations Some Analyses Constructing logical form Other Ways of Showing This π 1 [John had a lovely evening] Elaboration π 6 Narration π 2 π 5 [He had a great meal] [he won a dance competition] Elaboration π 7 Narration π 3 π 4 university-logo [he ate salmon] [he devoured cheese] Alex Lascarides SPNLP: SDRT
An extension of DRT rhetorical relations Some Analyses Constructing logical form Availability: You can attach things to the right frontier New information β can attach to: The label α = LAST ; 1 Any label γ such that: 2 Succ ( γ, α ) ; or 1 F ( l ) = R ( γ, α ) for some label l , where R is a subordinating 2 discourse relation ( Elaboration , Explanation or ⇓ ) We gloss this as α < γ Transitive Closure: 3 Any label γ that dominates α through a sequence of labels γ 1 , . . . , γ n such that α < γ 1 , γ 1 < γ 2 , . . . , γ n < γ . university-logo Alex Lascarides SPNLP: SDRT
An extension of DRT rhetorical relations Some Analyses Constructing logical form Available Anaphora (Not Parallel or Contrast ) Situation: β : K β ; K β contains anaphoric condition ϕ . Available antecedents are: in K β and DRS -accessible to ϕ 1 in K α , DRS -accessible to any condition in K α , and there is a 2 condition R ( α, γ ) in the SDRS such that γ = β or Succ ∗ ( γ, β ) (where R isn’t structural). Antecedent must be DRS -accessible on the right frontier university-logo Alex Lascarides SPNLP: SDRT
An extension of DRT rhetorical relations Some Analyses Constructing logical form Example: Uses Accessibility from DRT (9) Every farmer owns a donkey. ??He beats it. (10) A farmer owns a donkey. He beats it. π 1 , π 2 π 1 , π 2 x , y y x π 1 : π 1 : farmer ( x ) , donkey ( y ) ⇒ donkey ( y ) farmer ( x ) own ( x , y ) own ( x , y ) w , z w , z π 2 : beat ( w , z ) π 2 : beat ( w , z ) w =? , z =? w =? , z =? Background ( π 1 , π 2 ) Background ( π 1 , π 2 ) university-logo Contrast and Parallel work a bit differently: they make inaccessible things available . Alex Lascarides SPNLP: SDRT
An extension of DRT rhetorical relations Some Analyses Constructing logical form Improvement on DRT: The Dansville Example (7) π 1 John took an engine to Dansville. ( π 1 ) π 2 He picked up a boxcar ( π 2 ) π 3 It had a broken fuel pump ( π 3 ) DRT: Flat structure: An engine is accessible to it SDRT: Narration ( π 1 , π 2 ) ; So π 1 isn’t available to π 3 : R ( π 1 , π 3 ) can’t hold for any R So the engine is not an available antecedent to it university-logo Alex Lascarides SPNLP: SDRT
An extension of DRT rhetorical relations Some Analyses Constructing logical form Semantics: Veridical Relations Speech Acts!! Satisfaction Schema for Veridical Relations: ] M ◦ [ ] M ◦ [ f [ [ R ( π 1 , π 2 ) ] ] M g iff f [ [ K π 1 ] [ K π 2 ] [ φ R ( π 1 ,π 2 ) ] ] M g Veridical: Explanation , Elaboration , Background , Con- trast , Parallel , Narration , Result , Evidence . . . Non-veridical: Alternation , Consequence Divergent: Correction , Counterevidence university-logo Alex Lascarides SPNLP: SDRT
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