Recap from yesterday

1. Working with Discourse Representation TheoryPatrick Blackburn & Johan BosLecture 2Building Discourse Representation Structures

2. Recap from yesterday • Discourse representation theory [DRT] • Discourse representation structure [DRS] • Discourse referent • DRS conditions • Accessibility • Subordination

3. More about DRS • DRS can be viewed as a first–order language without explicit quantifiers

4. More about DRS • DRS can be viewed as a first–order language without explicit quantifiers • x [man(x) & smoke(x)]

5. More about DRS • DRS can be viewed as a first–order language without explicit quantifiers 

6. More about DRS • DRS can be viewed as a first–order language without explicit quantifiers  • x [man(x)  smoke(x)]

7. More about discourse referents • All noun phrases [NPs] introduce discourse referents • Indefinite NPs: a book • Definite NPs: the book • Proper name: Harry • Pronoun: she

8. More about discourse referents • Verbs introduce [event] discourse referents • Intransitive verbs: to sleep • Transitive verbs: to read

9. Accessibility 1    X

10. Accessibility 1 O -  - -   X

11. Accessibility 2  X  

12. Accessibility 2 O O  X - -  - 

13. Accessibility 3   X 

14. Accessibility 3 O -  - O  X - 

15. Accessibility 4   X 

16. Accessibility 4 O -  - O  X - 

17. Accessibility 5    X

18. Accessibility 5 O -  - O  O  X

19. Accessibility 6    X

20. Accessibility 6 O -  - O  O O  X

21. Subordination   

22. Subordination A  B C  D  E F

23. Subordination A subordinates B A subordinates C A subordinates D D subordinates E E subordinates F A  B C  D  E F

24. 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

25. 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.

26. Negation and indefinites • Vincent did not dance with a woman.She … 

27. Negation and definites • Vincent did not dance with the woman.She … 

28. Negation and proper names • Vincent did not dance with Mia.She … 

29. 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.

30. More about accessibility • Vincent did with some woman. She …

31. More about accessibility • Vincent did with every woman. She … 

32. More about accessibility • Vincent did with no woman. She … 

33. 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

34. Composing meaning • Frege’s principleThe meaning of a compound expression is a function of the meaning of its parts.

35. Composing DRSs [roughly] • Mia does not have a car • Mia • does not • have • a car 

36. Composing DRSs [roughly] • Mia does not have a car  • Mia • does not • have • a car 

37. 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

38. 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

39. 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

40. The Merge ; • We will introduce a new operator ; • The ; indicates a merge between two DRSs ; ( )

41. 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) ; ( )

42. A merge example • A boxer lost. • He died.

43. A merge example • A boxer lost. • He died. • A boxer lost.He died. ; ) (

44. Merge and accessibility • If (B1;B2) is a DRS, then • B1 subordinates B2 • I.e., discourse referents introduced in B1 are accessible from B2 ; ) (

45. Merge and variable binding • Which variables are bound, and which are free? ; ) ; ) ((

46. Merge and variable binding • Which variables are bound, and which are free? ; ) ; ) ((  free  free  free

47. Merge is associative • These two DRSs do not differ in meaning ; (( ( ; )) (( ; ) ; )

48. Merge is non-commutative • These two DRSs differ in meaning ; ( ) ; ( )

49. 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

50. Merge Reduction Example ; ( )