Discourse Representation Theory Building Discourse Representations

Transcription

1 and and Lehrstuhl für Künstliche Intelligenz Institut für Informatik Friedrich-Alexander-Universität Erlangen-Nürnberg 13. Januar Slides are mainly due to Johan Bos lecture on Semantics (GSLT)

2 Overview and last class: today:

3 Outline and 1 2 3

4 Discourse and DRT and Discourse: a sequence of several natural language sentences DRT is the theory that proposes a way to represent the meaning of discourse

5 Outline and 1 2 3

6 Overview of DRT and DRT employs a language based on boxlike structures called DRSs DRSs are Pictures (something like mental models )

7 Structures and A new discourse starts a new DRS: This DRS is meant to represent the meaning of an entire discourse When a new sentence ( A woman snorts ) is parsed, x the DRS is expanded: woman(x) snort(x) The x in the top of the box is a discourse referent The expressions woman(x) and snort(x) are DRS-conditions

8 of DRSs and If x1... xn are discourse referents, and C1... Cn are x1... xn C1 conditions, then... Cn is a DRS

9 Terms and of DRS-conditions and A term τ is either a constant or a discourse referent If R is a relation symbol of arity n, and tau τ 1... τ n are terms, then R(τ 1... τ n ) is a DRS-condition If τ 1 and τ 2 are terms then τ 1 = τ 2 is a DRS-condition If B is a DRS, then B is a DRS-condition If B 1 and B 2 are DRSs, then B 1 B 2 and B 1 B 2 are DRS-conditions

10 Outline and 1 2 3

11 DRSs and We know now what DRT is But how can we construct DRSs for discourses in a systematic and automatic way? There are various ways to do this we will explore the lambda-based method

12 Semantic Construction 2 and To build representations we need to: Specify the meanings of the words incomplete formulas (lexical semantics) Indicate where the missing information will come from (syntax) Provide means of combining parts of discourse (lexical semantics) Key ideas: Use lambda terms to specify lexical entries Make rules in the grammar specify which daughter is the function and which the argument Use implementation of lambda calculus to then yield the DRT(LF) of the mother node Design merge operation for DRSs 2 slide is mainly due to Alex Lascarides

13 Intuition behind λ and We first focus on λ-calculus. Lambdas talk about missing information, and where it is. The λ binds a variable The positions of a λ-bound variable in the formula mark where information is missing Replacing these variables with values fills in the missing information

14 DRSs with lambdas and We will use the lambda-calculus as a tool to build DRSs for sentences We will use λ to mark missing information in the DRS We call this combination λ-drt It will allow us to use a number of off-the-shelf tools, such as α, β-conversion.

15 : Nouns and proper names and boxer: λ x. λ binds variable x boxer(x) Position of x in boxer(x) marks where information is missing

16 The Merge and We will introduce a new operator merge ; The ; indicates a merge between two DRSs Discourse: A boxer loses. He dies. ( x boxer(x) lose(x) ; y die(y) y=x ) The merge is used to combine two DRSs into one larger DRS

17 Merge Reduction and Replacing merged DRSs for a new DRS by taking the union of the two universes and conditions: x y x y boxer(x) ( boxer(x) ; die(y) )= lose(x) lose(x) y=? die(y) y=? Accessibility Constraints x y boxer(x) lose(x) die(y) y=x The merge is the operation on DRSs we need to state in the lexical semantics

18 Example of Merge within : and Vincent: λ u.( x x=vincent ; u@ x)

19 : Nouns and proper names and boxer: λ x. Vincent: λ u.( boxer(x) x x=vincent ;u@ x)

20 : Determiners and a: λ p.λ q.(( x ;p@ x);q@ x) every: λ p.λ q.(( x ;p@x) q@ x)

21 : Verbs and dances: λ x. wins: λ x. admires: λ u.λ y. dance(x) win(x) admire(x,y)

22 and Sentence: A boxer wins. enrties: x a: λ p.λ q.(( ;p@ x);q@ x) boxer: λ x. wins: λ x. boxer(x) win(x) How do we put them together? α, β-conversions

23 β-conversion and β-conversion is the process of filling the missing information in place of lambda-bound variables: λ x. to woman(y)

24 Merge-reduction can only be applied after α-conversion and Consider the example: A woman walks and a woman talks x x x woman(x) ( woman(x) ; woman(x) )= walk(x) walk(x) talk(x) talk(x) This is of course not the result we want! Renaming mechanism is needed

25 α-conversion and α-conversion is the process of renaming bound variables: λ x. to λ y. boxer(x) boxer(y) These mean the same thing! λ x. to λ y. where λ argument boxer(x) functor Rename variables in functor so that they are all distinct from the variables in the argument. Rename variables in merged DRSs so that variables in one DRS are distinct from variables in the other. This is like using any variable in the lexical entries at

26 and Application and indicates how the missing information in lexical entries is filled: NP DET N NP DET@N Lexical semantic entry for DET functor Lexical semantic entry for N argument

27 Example and boxer. x λ p.λ q.(( ;p@ x);q@ x)@λ x. Blackboard 1. boxer(x)

28 Blackboard 2 and Every man dances Every: λ p.λ q.(( x ;p@x) q@x) man: λ x. dances: λ x. man(x) dance(x)