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Working with Discourse Representation Theory Patrick Blackburn & Johan Bos Lecture 2 Building Discourse Representation Structures. Recap from yesterday. Discourse representation theory [DRT] Discourse representation structure [DRS] Discourse referent DRS conditions Accessibility
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Working with Discourse Representation TheoryPatrick Blackburn & Johan BosLecture 2Building Discourse Representation Structures
Recap from yesterday • Discourse representation theory [DRT] • Discourse representation structure [DRS] • Discourse referent • DRS conditions • Accessibility • Subordination
More about DRS • DRS can be viewed as a first–order language without explicit quantifiers
More about DRS • DRS can be viewed as a first–order language without explicit quantifiers • x [man(x) & smoke(x)]
More about DRS • DRS can be viewed as a first–order language without explicit quantifiers
More about DRS • DRS can be viewed as a first–order language without explicit quantifiers • x [man(x) smoke(x)]
More about discourse referents • All noun phrases [NPs] introduce discourse referents • Indefinite NPs: a book • Definite NPs: the book • Proper name: Harry • Pronoun: she
More about discourse referents • Verbs introduce [event] discourse referents • Intransitive verbs: to sleep • Transitive verbs: to read
Accessibility 1 X
Accessibility 1 O - - - X
Accessibility 2 X
Accessibility 2 O O X - - -
Accessibility 3 X
Accessibility 3 O - - O X -
Accessibility 4 X
Accessibility 4 O - - O X -
Accessibility 5 X
Accessibility 5 O - - O O X
Accessibility 6 X
Accessibility 6 O - - O O O X
Subordination
Subordination A B C D E F
Subordination A subordinates B A subordinates C A subordinates D D subordinates E E subordinates F A B C D E F
Subordination A subordinates B A subordinates C A subordinates D D subordinates E E subordinates F A subordinates E A subordinates F ….. Etc. A B C D E F
DRT and negation • DRT predicts differences between the following DRSs wrt to the interpretation of the pronoun she • Vincent did not dance with the woman.She was pretty. • Vincent did not dance with Mia.She was pretty. • Vincent did not dance with a woman.X She was pretty.
Negation and indefinites • Vincent did not dance with a woman.She …
Negation and definites • Vincent did not dance with the woman.She …
Negation and proper names • Vincent did not dance with Mia.She …
More about accessibility • DRT predicts differences between the following DRSs wrt to the interpretation of the pronoun she • Vincent danced with some woman.She was pretty. • Vincent danced with every woman.X She was pretty. • Vincent danced with no woman.X She was pretty.
More about accessibility • Vincent did with some woman. She …
More about accessibility • Vincent did with every woman. She …
More about accessibility • Vincent did with no woman. She …
Today • We know now what DRT is, and we know what semantic representation is central to DRT • But how can we construct DRSs for English discourses in a systematic and automatic way? • There are various ways to do this – we will explore the lambda-based method
Composing meaning • Frege’s principleThe meaning of a compound expression is a function of the meaning of its parts.
Composing DRSs [roughly] • Mia does not have a car • Mia • does not • have • a car
Composing DRSs [roughly] • Mia does not have a car • Mia • does not • have • a car
What we need to do • We need a mechanism to combine two smaller DRSs into one larger DRS • Introduce Merge operator • Merge reduction • We need a mechanism to keep track of the naming of discourse referents • Introduce lambda operator and application • Beta conversion
What we also need • In addition, we need something that tells us how and which DRSs combine • In other words, we need syntactic structure • In this course, we will look at two formalisms of syntactic theory: • Phrase Structure Grammar • Categorial Grammar
Outline • Theory • DRS-Merging • The lambda calculus as a glue language for constructing DRSs • Practice • A simple fragment [without events] • A simple fragment with events • Implementation example
The Merge ; • We will introduce a new operator ; • The ; indicates a merge between two DRSs ; ( )
The Merge ; • We will introduce a new operator ; • The ; indicates a merge between two DRSs: • The merge is used to combine two DRSs into one larger DRS • If B1 and B2 are DRSs, then so is (B1;B2) ; ( )
A merge example • A boxer lost. • He died.
A merge example • A boxer lost. • He died. • A boxer lost.He died. ; ) (
Merge and accessibility • If (B1;B2) is a DRS, then • B1 subordinates B2 • I.e., discourse referents introduced in B1 are accessible from B2 ; ) (
Merge and variable binding • Which variables are bound, and which are free? ; ) ; ) ((
Merge and variable binding • Which variables are bound, and which are free? ; ) ; ) (( free free free
Merge is associative • These two DRSs do not differ in meaning ; (( ( ; )) (( ; ) ; )
Merge is non-commutative • These two DRSs differ in meaning ; ( ) ; ( )
Merge Reduction • Given a DRS with a merge, we can reduce it to a DRS without a merge • This is called merge reduction • Merge reduction is performed by taking the union of the universes and conditions • Merge reduction is subject to certain conditions
Merge Reduction Example ; ( )