Structures Informatiques et Logiques pour la Mod´ elisation Linguistique (MPRI 2.27.1 - second part) Philippe de Groote Inria 2012-2013 Philippe de Groote (Inria) MPRI 2.27.1 2012-2013 1 / 44
Discourse Analysis Introduction 1 Discourse representation theory 2 Discourse representation structures Interpretation Merging Anaphora resolution 3 Revisiting DRT 4 Left and right contexts Semantic interpretation of the sentences Semantic interpretation of the syntactic categories Type-theoretic dynamic logic 5 Aim Connectives Embedding of first order logic Philippe de Groote (Inria) MPRI 2.27.1 2012-2013 2 / 44
Introduction Discourse Analysis Introduction 1 Discourse representation theory 2 Discourse representation structures Interpretation Merging Anaphora resolution 3 Revisiting DRT 4 Left and right contexts Semantic interpretation of the sentences Semantic interpretation of the syntactic categories Type-theoretic dynamic logic 5 Aim Connectives Embedding of first order logic Philippe de Groote (Inria) MPRI 2.27.1 2012-2013 3 / 44
Introduction Examples A man entered the room. He switched on the light. I am the only one in this group who dares to say that I am wrong. Every farmer who owns a donkey beats it. A wolf might come in. It would eat you first. John does not have a car. He would not know where to park it. Either there is no bathroom in this apartment or it is in a funny place. The man who gives his paycheck to his wife is wiser than the man who gives it to his mistress. Philippe de Groote (Inria) MPRI 2.27.1 2012-2013 4 / 44
Discourse representation theory Discourse Analysis Introduction 1 Discourse representation theory 2 Discourse representation structures Interpretation Merging Anaphora resolution 3 Revisiting DRT 4 Left and right contexts Semantic interpretation of the sentences Semantic interpretation of the syntactic categories Type-theoretic dynamic logic 5 Aim Connectives Embedding of first order logic Philippe de Groote (Inria) MPRI 2.27.1 2012-2013 5 / 44
Discourse representation theory Discourse representation structures Discourse Analysis Introduction 1 Discourse representation theory 2 Discourse representation structures Interpretation Merging Anaphora resolution 3 Revisiting DRT 4 Left and right contexts Semantic interpretation of the sentences Semantic interpretation of the syntactic categories Type-theoretic dynamic logic 5 Aim Connectives Embedding of first order logic Philippe de Groote (Inria) MPRI 2.27.1 2012-2013 6 / 44
Discourse representation theory Discourse representation structures Definition Terms t ::= v | c Conditions C ::= ⊤ | Pt 1 . . . t n | v ˙ = t | v � = t | ¬ D Strucutures D ::= ( { v 1 , . . . , v n } , { C 1 , . . . , C m } ) Philippe de Groote (Inria) MPRI 2.27.1 2012-2013 7 / 44
Discourse representation theory Discourse representation structures Box notation v 1 · · · v n C 1 . . . C m Philippe de Groote (Inria) MPRI 2.27.1 2012-2013 8 / 44
Discourse representation theory Interpretation Discourse Analysis Introduction 1 Discourse representation theory 2 Discourse representation structures Interpretation Merging Anaphora resolution 3 Revisiting DRT 4 Left and right contexts Semantic interpretation of the sentences Semantic interpretation of the syntactic categories Type-theoretic dynamic logic 5 Aim Connectives Embedding of first order logic Philippe de Groote (Inria) MPRI 2.27.1 2012-2013 9 / 44
Discourse representation theory Interpretation Interpretation v 1 · · · v n C 1 is interpreted as ∃ v 1 . . . v n .C 1 ∧ . . . ∧ C m . . . C m Philippe de Groote (Inria) MPRI 2.27.1 2012-2013 10 / 44
Discourse representation theory Merging Discourse Analysis Introduction 1 Discourse representation theory 2 Discourse representation structures Interpretation Merging Anaphora resolution 3 Revisiting DRT 4 Left and right contexts Semantic interpretation of the sentences Semantic interpretation of the syntactic categories Type-theoretic dynamic logic 5 Aim Connectives Embedding of first order logic Philippe de Groote (Inria) MPRI 2.27.1 2012-2013 11 / 44
Discourse representation theory Merging Merging A man entered the room. He switched on the light x y x man x y man x • → entered the room x switched on the light y entered the room x y ˙ = x switched on the light y Every man loves a woman. ? He smiles at her u v x x man x man x u v • → y ¬ y ¬ smile at u v ¬ woman y ¬ woman y love x y love x y smile at u v Philippe de Groote (Inria) MPRI 2.27.1 2012-2013 12 / 44
Anaphora resolution Discourse Analysis Introduction 1 Discourse representation theory 2 Discourse representation structures Interpretation Merging Anaphora resolution 3 Revisiting DRT 4 Left and right contexts Semantic interpretation of the sentences Semantic interpretation of the syntactic categories Type-theoretic dynamic logic 5 Aim Connectives Embedding of first order logic Philippe de Groote (Inria) MPRI 2.27.1 2012-2013 13 / 44
Anaphora resolution Knowledge-poor approach Peter loves Mary. But she does not love him. It is John whom she loves. He is a nicer guy. Based on: morphological features, grammatical roles, discourse functions: theme (topic), rheme, ... Signaling the topic: stating it as the subject, using the passive voice — to turn an object into the subject, clefting (it is from Mary that I learned the news), periphrastic constructions (“as for”, “concerning”, “speaking of”, ...), dislocation, a.k.a. topicalization (Mary, I love her). Philippe de Groote (Inria) MPRI 2.27.1 2012-2013 14 / 44
Anaphora resolution Knowledge-poor approach + statistical training The utility (CDVU) shows you a LIST4250, LIST38PP, or LIST3820 file on your terminal for a format similar to that in which it will be printed Philippe de Groote (Inria) MPRI 2.27.1 2012-2013 15 / 44
Anaphora resolution Knowledge based approach John hid Bill’s keys. He was drunk. John hid Bill’s keys. He was playing a joke on him. Philippe de Groote (Inria) MPRI 2.27.1 2012-2013 16 / 44
Revisiting DRT Discourse Analysis Introduction 1 Discourse representation theory 2 Discourse representation structures Interpretation Merging Anaphora resolution 3 Revisiting DRT 4 Left and right contexts Semantic interpretation of the sentences Semantic interpretation of the syntactic categories Type-theoretic dynamic logic 5 Aim Connectives Embedding of first order logic Philippe de Groote (Inria) MPRI 2.27.1 2012-2013 17 / 44
Revisiting DRT Left and right contexts Discourse Analysis Introduction 1 Discourse representation theory 2 Discourse representation structures Interpretation Merging Anaphora resolution 3 Revisiting DRT 4 Left and right contexts Semantic interpretation of the sentences Semantic interpretation of the syntactic categories Type-theoretic dynamic logic 5 Aim Connectives Embedding of first order logic Philippe de Groote (Inria) MPRI 2.27.1 2012-2013 18 / 44
Revisiting DRT Left and right contexts Typing the left and right contexts Montague semantics is based on Church’s simple type theory, which provides a full hierarchy of functional types built upon two atomic types: e , the type of entities (a.k.a. individuals). t , the type of truth values (a.k.a. propositions). We add a third atomic type, c , which stands for the type of the left contexts. What about the type of the right contexts? left context right context ↓ � �� � � �� � • � �� � � �� � c → t c � �� � t Philippe de Groote (Inria) MPRI 2.27.1 2012-2013 19 / 44
Revisiting DRT Left and right contexts Updating and accessing the context : c nil :: : e → c → c : c → e sel Philippe de Groote (Inria) MPRI 2.27.1 2012-2013 20 / 44
Revisiting DRT Semantic interpretation of the sentences Discourse Analysis Introduction 1 Discourse representation theory 2 Discourse representation structures Interpretation Merging Anaphora resolution 3 Revisiting DRT 4 Left and right contexts Semantic interpretation of the sentences Semantic interpretation of the syntactic categories Type-theoretic dynamic logic 5 Aim Connectives Embedding of first order logic Philippe de Groote (Inria) MPRI 2.27.1 2012-2013 21 / 44
Revisiting DRT Semantic interpretation of the sentences Semantic interpretation of the sentences Let s be the syntactic category of sentences. Remember that we intend to abstract our notions of left and right contexts over the meaning of the sentences. [[ s ]] = c → ( c → t ) → t Philippe de Groote (Inria) MPRI 2.27.1 2012-2013 22 / 44
Revisiting DRT Semantic interpretation of the sentences Composition of two sentence interpretations [[ S 1 . S 2 ]] = λeφ. [[ S 1 ]] e ( λe ′ . [[ S 2 ]] e ′ φ ) Philippe de Groote (Inria) MPRI 2.27.1 2012-2013 23 / 44
Revisiting DRT Semantic interpretation of the sentences Back to DRT and DRSs Consider a DRS: x 1 . . . x n C 1 . . . C m To such a structure, corresponds the following λ -term of type c → ( c → t ) → t : λeφ. ∃ x 1 . . . x n . C 1 ∧ · · · ∧ C m ∧ φ e ′ where e ′ is a context made of e and of the variables x 1 , . . . , x n . Philippe de Groote (Inria) MPRI 2.27.1 2012-2013 24 / 44
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