1. Markus Egg, Alexander Koller, Joachim Niehren The Constraint Language for Lambda Structures Ventsislav Zhechev SfS, Universität Tübingen e-mail: vzhechev@sfs.uni-tuebingen.devzhechev@sfs.uni-tuebingen.de Ventsislav Zhechev SfS, Universität Tübingen e-mail: vzhechev@sfs.uni-tuebingen.devzhechev@sfs.uni-tuebingen.de

2. 19.01.20052 Agenda Introduction Motivation Basic Terms Elements of CLLS -terms -structures Discussed Phenomena Introduction Motivation Basic Terms Elements of CLLS -terms -structures Discussed Phenomena Introduction Motivation Basic Terms Introduction Motivation Basic Terms Elements of CLLS -terms -structures Discussed Phenomena Elements of CLLS -terms -structures Discussed Phenomena

3. 19.01.20053 Agenda (continued) Syntax and Semantics of CLLS Tree Structures -structures Dominance and Parallelism The CLLS Constraint Graphs Syntax and Semantics of CLLS Tree Structures -structures Dominance and Parallelism The CLLS Constraint Graphs Introduction Motivation Basic Terms Introduction Motivation Basic Terms Elements of CLLS -terms -structures Discussed Phenomena Elements of CLLS -terms -structures Discussed Phenomena

4. 19.01.20054 Agenda (continued) Interaction of Quantifiers, Anaphora and Ellipsis Quantifier Parallelism Strict/Sloppy Ambiguities Nested Ellipses A Complex Interaction Antecedent-Contained Ellipsis Interaction of Quantifiers, Anaphora and Ellipsis Quantifier Parallelism Strict/Sloppy Ambiguities Nested Ellipses A Complex Interaction Antecedent-Contained Ellipsis Introduction Motivation Basic Terms Introduction Motivation Basic Terms Elements of CLLS -terms -structures Discussed Phenomena Elements of CLLS -terms -structures Discussed Phenomena

5. 19.01.20055 Agenda (continued) The Syntax-Semantics Interface Grammar Semantic Construction An Example Computational Aspects Conclusion The Syntax-Semantics Interface Grammar Semantic Construction An Example Computational Aspects Conclusion Introduction Motivation Basic Terms Introduction Motivation Basic Terms Elements of CLLS -terms -structures Discussed Phenomena Elements of CLLS -terms -structures Discussed Phenomena

6. 19.01.20056 Introduction Motivation Basic Terms Introduction Motivation Basic Terms Introduction Motivation Basic Terms Introduction Motivation Basic Terms Introduction Motivation Basic Terms Linguistic Phenomena Scope Ambiguities Anaphora VP Ellipsis Underspecification Linguistic Phenomena Scope Ambiguities Anaphora VP Ellipsis Underspecification Elements of CLLS -terms -structures Discussed Phenomena Elements of CLLS -terms -structures Discussed Phenomena Introduction Motivation

7. 19.01.20057 Introduction Motivation Basic Terms Trees Underspecification Constraint Language for Lambda Structures: A Combination of Constraints Dominance Constraints Anaphoric Binding Constraints Parallelism Constraints -binding Constraints Trees Underspecification Constraint Language for Lambda Structures: A Combination of Constraints Dominance Constraints Anaphoric Binding Constraints Parallelism Constraints -binding Constraints Introduction Motivation Basic Terms Introduction Motivation Basic Terms Elements of CLLS -terms -structures Discussed Phenomena Elements of CLLS -terms -structures Discussed Phenomena Basic Terms

8. 19.01.20058 Introduction Motivation Basic Terms Introduction Motivation Basic Terms Elements of CLLS -terms -structures Discussed Phenomena Elements of CLLS -terms -structures Discussed Phenomena Every linguist attends a workshop. (a workshop)( x (every linguist)( y (attend x) y)) Types e  individuals t  truth values (0 or 1 / true or false)  one-place predicates >  two-place predicates etc. Every linguist attends a workshop. (a workshop)( x (every linguist)( y (attend x) y)) Types e  individuals t  truth values (0 or 1 / true or false)  one-place predicates >  two-place predicates etc. Elements of CLLS -terms -structures Discussed Phenomena Elements of CLLS -terms -structures Discussed Phenomena Syntax and Semantics of CLLS Tree Structures -structures Dominance and Parallelism The CLLS Constraint Graphs Syntax and Semantics of CLLS Tree Structures -structures Dominance and Parallelism The CLLS Constraint Graphs Elements of CLLS -terms -structures Discussed Phenomena Elements of CLLS -terms -structures Discussed Phenomena Elements of CLLS -terms

9. 19.01.20059 (a workshop)( x (every linguist)( y (attend x) y)) lam  -abstraction @  functional application var  bound variable  variable binding (a workshop)( x (every linguist)( y (attend x) y)) lam  -abstraction @  functional application var  bound variable  variable binding Elements of CLLS -terms -structures Discussed Phenomena Elements of CLLS -terms -structures Discussed Phenomena Syntax and Semantics of CLLS Tree Structures -structures Dominance and Parallelism The CLLS Constraint Graphs Syntax and Semantics of CLLS Tree Structures -structures Dominance and Parallelism The CLLS Constraint Graphs Elements of CLLS -terms -structures Discussed Phenomena Elements of CLLS -terms -structures Discussed Phenomena -structures attend

10. 19.01.200510 Scope Ambiguity Every linguist attends a workshop. (a workshop)( x (every linguist)( y (attend x) y)) (every linguist)( y (a workshop)( x (attend x) y))  dominance Scope Ambiguity Every linguist attends a workshop. (a workshop)( x (every linguist)( y (attend x) y)) (every linguist)( y (a workshop)( x (attend x) y))  dominance Elements of CLLS -terms -structures Discussed Phenomena Elements of CLLS -terms -structures Discussed Phenomena Syntax and Semantics of CLLS Tree Structures -structures Dominance and Parallelism The CLLS Constraint Graphs Syntax and Semantics of CLLS Tree Structures -structures Dominance and Parallelism The CLLS Constraint Graphs Elements of CLLS -terms -structures Discussed Phenomena Elements of CLLS -terms -structures Discussed Phenomena

11. 19.01.200511 Elements of CLLS -terms -structures Discussed Phenomena Elements of CLLS -terms -structures Discussed Phenomena VP Ellipsis Every man sleeps, and so does Mary. Parallelism Constraint: X 1 /X 2 ~Y 1 /Y 2 VP Ellipsis Every man sleeps, and so does Mary. Parallelism Constraint: X 1 /X 2 ~Y 1 /Y 2 Syntax and Semantics of CLLS Tree Structures -structures Dominance and Parallelism The CLLS Constraint Graphs Syntax and Semantics of CLLS Tree Structures -structures Dominance and Parallelism The CLLS Constraint Graphs

12. 19.01.200512 Elements of CLLS -terms -structures Discussed Phenomena Elements of CLLS -terms -structures Discussed Phenomena Anaphora John i said he i j liked his j mother. ana  anaphora  anaphoric link Anaphora John i said he i j liked his j mother. ana  anaphora  anaphoric link Syntax and Semantics of CLLS Tree Structures -structures Dominance and Parallelism The CLLS Constraint Graphs Syntax and Semantics of CLLS Tree Structures -structures Dominance and Parallelism The CLLS Constraint Graphs

13. 19.01.200513 Elements of CLLS -terms -structures Discussed Phenomena Elements of CLLS -terms -structures Discussed Phenomena The Capturing Problem Variable binding in -terms is usually indicated by using variable names, i.e. x binds all occurrences of x in its scope Possible Problems: -calculus has to exclude the capturing of free variables by unintended binders Problems with constraints used for scope ambiguities Problems in the presence of parallelism constraints The Capturing Problem Variable binding in -terms is usually indicated by using variable names, i.e. x binds all occurrences of x in its scope Possible Problems: -calculus has to exclude the capturing of free variables by unintended binders Problems with constraints used for scope ambiguities Problems in the presence of parallelism constraints Syntax and Semantics of CLLS Tree Structures -structures Dominance and Parallelism The CLLS Constraint Graphs Syntax and Semantics of CLLS Tree Structures -structures Dominance and Parallelism The CLLS Constraint Graphs

14. 19.01.200514 Elements of CLLS -terms -structures Discussed Phenomena Elements of CLLS -terms -structures Discussed Phenomena Syntax and Semantics of CLLS Tree Structures -structures Dominance and Parallelism The CLLS Constraint Graphs Syntax and Semantics of CLLS Tree Structures -structures Dominance and Parallelism The CLLS Constraint Graphs Trees and Tree Structures The Algebra of Trees Let  be a set of function symbols, f, g, a, b Each function symbol f has fixed arity We write f k for a function symbol f with arity k ≥ 0 We define tree as a ground term built from a set of function symbols We define path as a word over ℕ (the natural numbers) We identify each node in a tree with the path from the root to this node The empty word, , identifies the root Concatenation is written as  A word  is a prefix of , iff there is a word  1 such that  =  1 Trees and Tree Structures The Algebra of Trees Let  be a set of function symbols, f, g, a, b Each function symbol f has fixed arity We write f k for a function symbol f with arity k ≥ 0 We define tree as a ground term built from a set of function symbols We define path as a word over ℕ (the natural numbers) We identify each node in a tree with the path from the root to this node The empty word, , identifies the root Concatenation is written as  A word  is a prefix of , iff there is a word  1 such that  =  1 Syntax and Semantics of CLLS Tree Structures -structures Dominance and Parallelism The CLLS Constraint Graphs Syntax and Semantics of CLLS Tree Structures -structures Dominance and Parallelism The CLLS Constraint Graphs Syntax and Semantics of CLLS Tree Structures -structures Dominance and Parallelism The CLLS Constraint Graphs Syntax and Semantics of CLLS Tree Structures -structures Dominance and Parallelism The CLLS Constraint Graphs Interaction of Quantifiers, Anaphora and Ellipsis Quantifier Parallelism Strict/Sloppy Ambiguities Nested Ellipses A Complex Interaction Antecedent-Contained Ellipsis Interaction of Quantifiers, Anaphora and Ellipsis Quantifier Parallelism Strict/Sloppy Ambiguities Nested Ellipses A Complex Interaction Antecedent-Contained Ellipsis Syntax and Semantics of CLLS Tree Structures

15. 19.01.200515 Syntax and Semantics of CLLS Tree Structures -structures Dominance and Parallelism The CLLS Constraint Graphs Syntax and Semantics of CLLS Tree Structures -structures Dominance and Parallelism The CLLS Constraint Graphs Tree Structures tree domain  is a finite nonempty set of nodes, which is prefix closed (    ) and closed under left siblings (  i    j  for all 1≤j<i) tree structure is defined as follows: Given nodes  0,...,  n, we write  0 :f(  1,...,  n ) for (  0,  1,...,  n )  :f Tree Structures tree domain  is a finite nonempty set of nodes, which is prefix closed (    ) and closed under left siblings (  i    j  for all 1≤j<i) tree structure is defined as follows: Given nodes  0,...,  n, we write  0 :f(  1,...,  n ) for (  0,  1,...,  n )  :f Interaction of Quantifiers, Anaphora and Ellipsis Quantifier Parallelism Strict/Sloppy Ambiguities Nested Ellipses A Complex Interaction Antecedent-Contained Ellipsis Interaction of Quantifiers, Anaphora and Ellipsis Quantifier Parallelism Strict/Sloppy Ambiguities Nested Ellipses A Complex Interaction Antecedent-Contained Ellipsis

16. 19.01.200516 Tree Structures and -structures Formalization For -structures we assume: {var 0, ana 0, lam 1, @ 2 }   We define -structures as follows: We draw -structures as tree-like graphs Tree Structures and -structures Formalization For -structures we assume: {var 0, ana 0, lam 1, @ 2 }   We define -structures as follows: We draw -structures as tree-like graphs Syntax and Semantics of CLLS Tree Structures -structures Dominance and Parallelism The CLLS Constraint Graphs Syntax and Semantics of CLLS Tree Structures -structures Dominance and Parallelism The CLLS Constraint Graphs Syntax and Semantics of CLLS Tree Structures -structures Dominance and Parallelism The CLLS Constraint Graphs Syntax and Semantics of CLLS Tree Structures -structures Dominance and Parallelism The CLLS Constraint Graphs -structures Interaction of Quantifiers, Anaphora and Ellipsis Quantifier Parallelism Strict/Sloppy Ambiguities Nested Ellipses A Complex Interaction Antecedent-Contained Ellipsis Interaction of Quantifiers, Anaphora and Ellipsis Quantifier Parallelism Strict/Sloppy Ambiguities Nested Ellipses A Complex Interaction Antecedent-Contained Ellipsis

17. 19.01.200517 Dominance Let  be a -structure and ,  two of its nodes. We say that  dominates  (  ⊲ *  ), if  lies above , i.e.  is a prefix of  Dominance is a partial order on the domain of  and it is reflexive, transitive and antisymmetric Parallelism We call any pair  /  of nodes ,  in  with  ⊲ *  a segment of , where  is called the root and  the hole of the segment We define: Dominance Let  be a -structure and ,  two of its nodes. We say that  dominates  (  ⊲ *  ), if  lies above , i.e.  is a prefix of  Dominance is a partial order on the domain of  and it is reflexive, transitive and antisymmetric Parallelism We call any pair  /  of nodes ,  in  with  ⊲ *  a segment of , where  is called the root and  the hole of the segment We define: Syntax and Semantics of CLLS Tree Structures -structures Dominance and Parallelism The CLLS Constraint Graphs Syntax and Semantics of CLLS Tree Structures -structures Dominance and Parallelism The CLLS Constraint Graphs Syntax and Semantics of CLLS Tree Structures -structures Dominance and Parallelism The CLLS Constraint Graphs Syntax and Semantics of CLLS Tree Structures -structures Dominance and Parallelism The CLLS Constraint Graphs Dominance and Parallelism Interaction of Quantifiers, Anaphora and Ellipsis Quantifier Parallelism Strict/Sloppy Ambiguities Nested Ellipses A Complex Interaction Antecedent-Contained Ellipsis Interaction of Quantifiers, Anaphora and Ellipsis Quantifier Parallelism Strict/Sloppy Ambiguities Nested Ellipses A Complex Interaction Antecedent-Contained Ellipsis

18. 19.01.200518 Syntax and Semantics of CLLS Tree Structures -structures Dominance and Parallelism The CLLS Constraint Graphs Syntax and Semantics of CLLS Tree Structures -structures Dominance and Parallelism The CLLS Constraint Graphs Correspondence Functions between segments: Parallelism Relation: Correspondence Functions between segments: Parallelism Relation: Interaction of Quantifiers, Anaphora and Ellipsis Quantifier Parallelism Strict/Sloppy Ambiguities Nested Ellipses A Complex Interaction Antecedent-Contained Ellipsis Interaction of Quantifiers, Anaphora and Ellipsis Quantifier Parallelism Strict/Sloppy Ambiguities Nested Ellipses A Complex Interaction Antecedent-Contained Ellipsis

19. 19.01.200519 Syntax and Semantics of CLLS Tree Structures -structures Dominance and Parallelism The CLLS Constraint Graphs Syntax and Semantics of CLLS Tree Structures -structures Dominance and Parallelism The CLLS Constraint Graphs Interaction of Quantifiers, Anaphora and Ellipsis Quantifier Parallelism Strict/Sloppy Ambiguities Nested Ellipses A Complex Interaction Antecedent-Contained Ellipsis Interaction of Quantifiers, Anaphora and Ellipsis Quantifier Parallelism Strict/Sloppy Ambiguities Nested Ellipses A Complex Interaction Antecedent-Contained Ellipsis

20. 19.01.200520 Interaction of Quantifiers, Anaphora and Ellipsis Quantifier Parallelism Strict/Sloppy Ambiguities Nested Ellipses A Complex Interaction Antecedent-Contained Ellipsis Interaction of Quantifiers, Anaphora and Ellipsis Quantifier Parallelism Strict/Sloppy Ambiguities Nested Ellipses A Complex Interaction Antecedent-Contained Ellipsis We assume an infinite set of node variables, ranged over X, X i, Y, etc. We pick relation symbols for all relations defined so far Finally we define CLLS with the following abstract syntax: The Semantics of CLLS is defined by interpretation of constraints over the class of -structures: A pair of a -structure  and a variable assignment  into the domain of  satisfies a constraint , iff it satisfies each atomic conjunct of it We call ( ,  ) a solution of  in this case We assume an infinite set of node variables, ranged over X, X i, Y, etc. We pick relation symbols for all relations defined so far Finally we define CLLS with the following abstract syntax: The Semantics of CLLS is defined by interpretation of constraints over the class of -structures: A pair of a -structure  and a variable assignment  into the domain of  satisfies a constraint , iff it satisfies each atomic conjunct of it We call ( ,  ) a solution of  in this case Syntax and Semantics of CLLS Tree Structures -structures Dominance and Parallelism The CLLS Constraint Graphs Syntax and Semantics of CLLS Tree Structures -structures Dominance and Parallelism The CLLS Constraint Graphs Syntax and Semantics of CLLS Tree Structures -structures Dominance and Parallelism The CLLS Constraint Graphs Syntax and Semantics of CLLS Tree Structures -structures Dominance and Parallelism The CLLS Constraint Graphs The CLLS

21. 19.01.200521 CLLS Constraints are usually hard to read in the standard syntax. That is why we will use constraint graphs for presenting the constraints For Example: CLLS Constraints are usually hard to read in the standard syntax. That is why we will use constraint graphs for presenting the constraints For Example: Syntax and Semantics of CLLS Tree Structures -structures Dominance and Parallelism The CLLS Constraint Graphs Syntax and Semantics of CLLS Tree Structures -structures Dominance and Parallelism The CLLS Constraint Graphs Syntax and Semantics of CLLS Tree Structures -structures Dominance and Parallelism The CLLS Constraint Graphs Syntax and Semantics of CLLS Tree Structures -structures Dominance and Parallelism The CLLS Constraint Graphs Interaction of Quantifiers, Anaphora and Ellipsis Quantifier Parallelism Strict/Sloppy Ambiguities Nested Ellipses A Complex Interaction Antecedent-Contained Ellipsis Interaction of Quantifiers, Anaphora and Ellipsis Quantifier Parallelism Strict/Sloppy Ambiguities Nested Ellipses A Complex Interaction Antecedent-Contained Ellipsis

22. 19.01.200522 Interaction of Quantifiers, Anaphora and Ellipsis Quantifier Parallelism Strict/Sloppy Ambiguities Nested Ellipses A Complex Interaction Antecedent-Contained Ellipsis Interaction of Quantifiers, Anaphora and Ellipsis Quantifier Parallelism Strict/Sloppy Ambiguities Nested Ellipses A Complex Interaction Antecedent-Contained Ellipsis The Syntax-Semantics Interface Grammar Semantic Construction An Example Computational Aspects Conclusion The Syntax-Semantics Interface Grammar Semantic Construction An Example Computational Aspects Conclusion Syntax and Semantics of CLLS Tree Structures -structures Dominance and Parallelism The CLLS Constraint Graphs Syntax and Semantics of CLLS Tree Structures -structures Dominance and Parallelism The CLLS Constraint Graphs Throughout the chapter we assume a fixed signature:  ={@ 2, lam 1, var 0, ana 0, before 2, mary 0, read 0,...} We follow the convention that proper nouns are always analyzed as constants of type e, except as contrasting elements in ellipses where the other contrasting element is a quantifier Throughout the chapter we assume a fixed signature:  ={@ 2, lam 1, var 0, ana 0, before 2, mary 0, read 0,...} We follow the convention that proper nouns are always analyzed as constants of type e, except as contrasting elements in ellipses where the other contrasting element is a quantifier Interaction of Quantifiers, Anaphora and Ellipsis Quantifier Parallelism Strict/Sloppy Ambiguities Nested Ellipses A Complex Interaction Antecedent-Contained Ellipsis Interaction of Quantifiers, Anaphora and Ellipsis Quantifier Parallelism Strict/Sloppy Ambiguities Nested Ellipses A Complex Interaction Antecedent-Contained Ellipsis

23. 19.01.200523 The Syntax-Semantics Interface Grammar Semantic Construction An Example Computational Aspects Conclusion The Syntax-Semantics Interface Grammar Semantic Construction An Example Computational Aspects Conclusion Every linguist attends a workshop. Every computer scientist does, too. The pair of sentences has three possible readings, although it may seem that there are four The CLLS constraint for the two sentences looks like this: Every linguist attends a workshop. Every computer scientist does, too. The pair of sentences has three possible readings, although it may seem that there are four The CLLS constraint for the two sentences looks like this: Interaction of Quantifiers, Anaphora and Ellipsis Quantifier Parallelism Strict/Sloppy Ambiguities Nested Ellipses A Complex Interaction Antecedent-Contained Ellipsis Interaction of Quantifiers, Anaphora and Ellipsis Quantifier Parallelism Strict/Sloppy Ambiguities Nested Ellipses A Complex Interaction Antecedent-Contained Ellipsis Quantifier Parallelism Interaction of Quantifiers, Anaphora and Ellipsis Quantifier Parallelism Strict/Sloppy Ambiguities Nested Ellipses A Complex Interaction Antecedent-Contained Ellipsis Interaction of Quantifiers, Anaphora and Ellipsis Quantifier Parallelism Strict/Sloppy Ambiguities Nested Ellipses A Complex Interaction Antecedent-Contained Ellipsis

24. 19.01.200524 The Syntax-Semantics Interface Grammar Semantic Construction An Example Computational Aspects Conclusion The Syntax-Semantics Interface Grammar Semantic Construction An Example Computational Aspects Conclusion John likes his mother, and Bill does too. The sentence has two readings: strict (Bill likes John’s mother) and sloppy (Bill likes Bill’s mother) We describe the meaning of the sentence using parallelism and anaphoric linking constraints: John likes his mother, and Bill does too. The sentence has two readings: strict (Bill likes John’s mother) and sloppy (Bill likes Bill’s mother) We describe the meaning of the sentence using parallelism and anaphoric linking constraints: Interaction of Quantifiers, Anaphora and Ellipsis Quantifier Parallelism Strict/Sloppy Ambiguities Nested Ellipses A Complex Interaction Antecedent-Contained Ellipsis Interaction of Quantifiers, Anaphora and Ellipsis Quantifier Parallelism Strict/Sloppy Ambiguities Nested Ellipses A Complex Interaction Antecedent-Contained Ellipsis Strict/Sloppy Ambiguities Interaction of Quantifiers, Anaphora and Ellipsis Quantifier Parallelism Strict/Sloppy Ambiguities Nested Ellipses A Complex Interaction Antecedent-Contained Ellipsis Interaction of Quantifiers, Anaphora and Ellipsis Quantifier Parallelism Strict/Sloppy Ambiguities Nested Ellipses A Complex Interaction Antecedent-Contained Ellipsis

25. 19.01.200525 Interaction of Quantifiers, Anaphora and Ellipsis Quantifier Parallelism Strict/Sloppy Ambiguities Nested Ellipses A Complex Interaction Antecedent-Contained Ellipsis Interaction of Quantifiers, Anaphora and Ellipsis Quantifier Parallelism Strict/Sloppy Ambiguities Nested Ellipses A Complex Interaction Antecedent-Contained Ellipsis The Syntax-Semantics Interface Grammar Semantic Construction An Example Computational Aspects Conclusion The Syntax-Semantics Interface Grammar Semantic Construction An Example Computational Aspects Conclusion According to the parallelism constraint the tree part of the -structure below X t is the same as the one below X s, except for the contrasting elements, as follows: This is yet not a complete -structure, because the anaphor at X a ’ doesn’t have an antecedent According to the parallelism constraint the tree part of the -structure below X t is the same as the one below X s, except for the contrasting elements, as follows: This is yet not a complete -structure, because the anaphor at X a ’ doesn’t have an antecedent

26. 19.01.200526 The Syntax-Semantics Interface Grammar Semantic Construction An Example Computational Aspects Conclusion The Syntax-Semantics Interface Grammar Semantic Construction An Example Computational Aspects Conclusion John revised his paper before the teacher did, and so did Bill. This sentence comprises nested ellipsis: the source clause of the ellipsis is elliptical itself The sentence is further complicated by the presence of the anaphor, which induces a complex strict/sloppy ambiguity We follow Dalrymple et al. (1991) in assuming five readings for the sentence John revised his paper before the teacher did, and so did Bill. This sentence comprises nested ellipsis: the source clause of the ellipsis is elliptical itself The sentence is further complicated by the presence of the anaphor, which induces a complex strict/sloppy ambiguity We follow Dalrymple et al. (1991) in assuming five readings for the sentence Interaction of Quantifiers, Anaphora and Ellipsis Quantifier Parallelism Strict/Sloppy Ambiguities Nested Ellipses A Complex Interaction Antecedent-Contained Ellipsis Interaction of Quantifiers, Anaphora and Ellipsis Quantifier Parallelism Strict/Sloppy Ambiguities Nested Ellipses A Complex Interaction Antecedent-Contained Ellipsis Nested Ellipses Interaction of Quantifiers, Anaphora and Ellipsis Quantifier Parallelism Strict/Sloppy Ambiguities Nested Ellipses A Complex Interaction Antecedent-Contained Ellipsis Interaction of Quantifiers, Anaphora and Ellipsis Quantifier Parallelism Strict/Sloppy Ambiguities Nested Ellipses A Complex Interaction Antecedent-Contained Ellipsis

27. 19.01.200527 Interaction of Quantifiers, Anaphora and Ellipsis Quantifier Parallelism Strict/Sloppy Ambiguities Nested Ellipses A Complex Interaction Antecedent-Contained Ellipsis Interaction of Quantifiers, Anaphora and Ellipsis Quantifier Parallelism Strict/Sloppy Ambiguities Nested Ellipses A Complex Interaction Antecedent-Contained Ellipsis The Syntax-Semantics Interface Grammar Semantic Construction An Example Computational Aspects Conclusion The Syntax-Semantics Interface Grammar Semantic Construction An Example Computational Aspects Conclusion All five readings are represented by the following constraint:

28. 19.01.200528 The Syntax-Semantics Interface Grammar Semantic Construction An Example Computational Aspects Conclusion The Syntax-Semantics Interface Grammar Semantic Construction An Example Computational Aspects Conclusion Mary read a book she liked before Sue did. The sentence has three readings In the first reading the indefinite NP a book she liked outscopes both clauses The second and the third reading arise from a strict/sloppy ambiguity that occurs if the operator before outscopes the indefinite Here is a constraint describing the readings: Mary read a book she liked before Sue did. The sentence has three readings In the first reading the indefinite NP a book she liked outscopes both clauses The second and the third reading arise from a strict/sloppy ambiguity that occurs if the operator before outscopes the indefinite Here is a constraint describing the readings: Interaction of Quantifiers, Anaphora and Ellipsis Quantifier Parallelism Strict/Sloppy Ambiguities Nested Ellipses A Complex Interaction Antecedent-Contained Ellipsis Interaction of Quantifiers, Anaphora and Ellipsis Quantifier Parallelism Strict/Sloppy Ambiguities Nested Ellipses A Complex Interaction Antecedent-Contained Ellipsis A Complex Interaction Interaction of Quantifiers, Anaphora and Ellipsis Quantifier Parallelism Strict/Sloppy Ambiguities Nested Ellipses A Complex Interaction Antecedent-Contained Ellipsis Interaction of Quantifiers, Anaphora and Ellipsis Quantifier Parallelism Strict/Sloppy Ambiguities Nested Ellipses A Complex Interaction Antecedent-Contained Ellipsis

29. 19.01.200529 Schematic representations of the solutions: First reading: Second reading: Third reading: Schematic representations of the solutions: First reading: Second reading: Third reading: Interaction of Quantifiers, Anaphora and Ellipsis Quantifier Parallelism Strict/Sloppy Ambiguities Nested Ellipses A Complex Interaction Antecedent-Contained Ellipsis Interaction of Quantifiers, Anaphora and Ellipsis Quantifier Parallelism Strict/Sloppy Ambiguities Nested Ellipses A Complex Interaction Antecedent-Contained Ellipsis The Syntax-Semantics Interface Grammar Semantic Construction An Example Computational Aspects Conclusion The Syntax-Semantics Interface Grammar Semantic Construction An Example Computational Aspects Conclusion

30. 19.01.200530 The Syntax-Semantics Interface Grammar Semantic Construction An Example Computational Aspects Conclusion The Syntax-Semantics Interface Grammar Semantic Construction An Example Computational Aspects Conclusion John greeted every person that Max did. The problem is that the ellipsis is contained in the VP it refers to In CLLS the meaning of the sentence is described as follows: John greeted every person that Max did. The problem is that the ellipsis is contained in the VP it refers to In CLLS the meaning of the sentence is described as follows: Interaction of Quantifiers, Anaphora and Ellipsis Quantifier Parallelism Strict/Sloppy Ambiguities Nested Ellipses A Complex Interaction Antecedent-Contained Ellipsis Interaction of Quantifiers, Anaphora and Ellipsis Quantifier Parallelism Strict/Sloppy Ambiguities Nested Ellipses A Complex Interaction Antecedent-Contained Ellipsis Interaction of Quantifiers, Anaphora and Ellipsis Quantifier Parallelism Strict/Sloppy Ambiguities Nested Ellipses A Complex Interaction Antecedent-Contained Ellipsis Interaction of Quantifiers, Anaphora and Ellipsis Quantifier Parallelism Strict/Sloppy Ambiguities Nested Ellipses A Complex Interaction Antecedent-Contained Ellipsis

31. 19.01.200531 Interaction of Quantifiers, Anaphora and Ellipsis Quantifier Parallelism Strict/Sloppy Ambiguities Nested Ellipses A Complex Interaction Antecedent-Contained Ellipsis Interaction of Quantifiers, Anaphora and Ellipsis Quantifier Parallelism Strict/Sloppy Ambiguities Nested Ellipses A Complex Interaction Antecedent-Contained Ellipsis The Syntax-Semantics Interface Grammar Semantic Construction An Example Computational Aspects Conclusion The Syntax-Semantics Interface Grammar Semantic Construction An Example Computational Aspects Conclusion There is one problem with this analysis: the notion of binding equivalence as defined is too strong a restriction for ACD The redefinition is given as: There is one problem with this analysis: the notion of binding equivalence as defined is too strong a restriction for ACD The redefinition is given as:

32. 19.01.200532 Interaction of Quantifiers, Anaphora and Ellipsis Quantifier Parallelism Strict/Sloppy Ambiguities Nested Ellipses A Complex Interaction Antecedent-Contained Ellipsis Interaction of Quantifiers, Anaphora and Ellipsis Quantifier Parallelism Strict/Sloppy Ambiguities Nested Ellipses A Complex Interaction Antecedent-Contained Ellipsis The Syntax-Semantics Interface Grammar Semantic Construction An Example Computational Aspects Conclusion The Syntax-Semantics Interface Grammar Semantic Construction An Example Computational Aspects Conclusion The preconditions for the two branches of the definitions are given here as (a) and (b) respectively: This analysis also accounts for the difference between the following two sentences (the first one lacking one of the two readings of the second sentence): John wants Bill to read everything that Max does. John wants Bill to read everything Max wants him to read. The preconditions for the two branches of the definitions are given here as (a) and (b) respectively: This analysis also accounts for the difference between the following two sentences (the first one lacking one of the two readings of the second sentence): John wants Bill to read everything that Max does. John wants Bill to read everything Max wants him to read.

33. 19.01.200533 Interaction of Quantifiers, Anaphora and Ellipsis Quantifier Parallelism Strict/Sloppy Ambiguities Nested Ellipses A Complex Interaction Antecedent-Contained Ellipsis Interaction of Quantifiers, Anaphora and Ellipsis Quantifier Parallelism Strict/Sloppy Ambiguities Nested Ellipses A Complex Interaction Antecedent-Contained Ellipsis The Syntax-Semantics Interface Grammar Semantic Construction An Example The Syntax-Semantics Interface Grammar Semantic Construction An Example The Syntax-Semantics Interface Grammar Semantic Construction An Example The Syntax-Semantics Interface Grammar Semantic Construction An Example Phrase Structure Rules: The Lexicon is defined by a relation Lex, which relates words W and lexical categories  {Det, N, IV, TV, SV, RP,...}. Terminal productions (a13) expand lexical categories to words of this category Phrase Structure Rules: The Lexicon is defined by a relation Lex, which relates words W and lexical categories  {Det, N, IV, TV, SV, RP,...}. Terminal productions (a13) expand lexical categories to words of this category The Syntax-Semantics Interface Grammar The Syntax-Semantics Interface Grammar Semantic Construction An Example Computational Aspects Conclusion The Syntax-Semantics Interface Grammar Semantic Construction An Example Computational Aspects Conclusion Computational Aspects Conclusion Computational Aspects Conclusion

34. 19.01.200534 The Syntax-Semantics Interface should factor out as much of the constraint construction as possible into the interface rules Most of the lexical entries introduce just one labeling constraint For each node in the syntax tree a constraint is generated; the constraint of the whole tree is the conjunction of these subconstraints Each node  ℕ * in the syntax tree is associated with two variables, X  s (the local scope domain of  ) and X  r (the root of the subconstraint for  ) The Syntax-Semantics Interface should factor out as much of the constraint construction as possible into the interface rules Most of the lexical entries introduce just one labeling constraint For each node in the syntax tree a constraint is generated; the constraint of the whole tree is the conjunction of these subconstraints Each node  ℕ * in the syntax tree is associated with two variables, X  s (the local scope domain of  ) and X  r (the root of the subconstraint for  ) Semantic Construction The Syntax-Semantics Interface Grammar Semantic Construction An Example The Syntax-Semantics Interface Grammar Semantic Construction An Example The Syntax-Semantics Interface Grammar Semantic Construction An Example The Syntax-Semantics Interface Grammar Semantic Construction An Example Computational Aspects Conclusion Computational Aspects Conclusion

35. 19.01.200535 The Syntax-Semantics Interface Grammar Semantic Construction An Example The Syntax-Semantics Interface Grammar Semantic Construction An Example We add a constraint X  s ⊲ *X  r for each determiner  which is not an indefinite. We also add this constraint whenever  is a verb We associate with each NP an index i that is used in the syntactic tree for coindexation with a variable X i The variables associated with syntactic nodes are related by the following rules: We add a constraint X  s ⊲ *X  r for each determiner  which is not an indefinite. We also add this constraint whenever  is a verb We associate with each NP an index i that is used in the syntactic tree for coindexation with a variable X i The variables associated with syntactic nodes are related by the following rules: Computational Aspects Conclusion Computational Aspects Conclusion

36. 19.01.200536 The Syntax-Semantics Interface Grammar Semantic Construction An Example The Syntax-Semantics Interface Grammar Semantic Construction An Example Computational Aspects Conclusion Computational Aspects Conclusion

37. 19.01.200537 The Syntax-Semantics Interface Grammar Semantic Construction An Example The Syntax-Semantics Interface Grammar Semantic Construction An Example Computational Aspects Conclusion Computational Aspects Conclusion

38. 19.01.200538 The Syntax-Semantics Interface Grammar Semantic Construction An Example The Syntax-Semantics Interface Grammar Semantic Construction An Example Computational Aspects Conclusion Computational Aspects Conclusion

39. 19.01.200539 The Syntax-Semantics Interface Grammar Semantic Construction An Example The Syntax-Semantics Interface Grammar Semantic Construction An Example The complete constraint which the interface produces is the conjunction of all the local constraints we just mentioned, plus the labeling constraints for the lexical entries, of the type X  r :sleep Exceptions to this rule: The elliptic does (too) does not add a labeling constraint; its semantics is determined via a parallelism constraint Whenever coindexation signifies a relation between an anaphor  ’ and its antecedent , we add the constraint X  r =X i, when we process  and the constraint X  ’ r :ana  ante(X  ’ r )=X i when we process  ’ The complete constraint which the interface produces is the conjunction of all the local constraints we just mentioned, plus the labeling constraints for the lexical entries, of the type X  r :sleep Exceptions to this rule: The elliptic does (too) does not add a labeling constraint; its semantics is determined via a parallelism constraint Whenever coindexation signifies a relation between an anaphor  ’ and its antecedent , we add the constraint X  r =X i, when we process  and the constraint X  ’ r :ana  ante(X  ’ r )=X i when we process  ’ Computational Aspects Conclusion Computational Aspects Conclusion

40. 19.01.200540 The Syntax-Semantics Interface Grammar Semantic Construction An Example The Syntax-Semantics Interface Grammar Semantic Construction An Example The constraint for a relative pronoun with index i at  is X  r =X i  X i :var; and the constraint for the corresponding trace (say, at  ’) is X  ’ r =X i. This, together with rule (b11), enforces correct binding of the trace The constraints for possessive pronouns, such as his, are as follows: The constraint for a relative pronoun with index i at  is X  r =X i  X i :var; and the constraint for the corresponding trace (say, at  ’) is X  ’ r =X i. This, together with rule (b11), enforces correct binding of the trace The constraints for possessive pronouns, such as his, are as follows: Computational Aspects Conclusion Computational Aspects Conclusion

41. 19.01.200541 Every linguist attends a workshop. First the lexical elements introduce several labeling constraints: X 11 r :every, X 121 r :linguist, X 21 r :attend, X 221 r :a, X 2221 r :workshop Every linguist attends a workshop. First the lexical elements introduce several labeling constraints: X 11 r :every, X 121 r :linguist, X 21 r :attend, X 221 r :a, X 2221 r :workshop An Example The Syntax-Semantics Interface Grammar Semantic Construction An Example The Syntax-Semantics Interface Grammar Semantic Construction An Example The Syntax-Semantics Interface Grammar Semantic Construction An Example The Syntax-Semantics Interface Grammar Semantic Construction An Example Computational Aspects Conclusion Computational Aspects Conclusion

42. 19.01.200542 The Syntax-Semantics Interface Grammar Semantic Construction An Example The Syntax-Semantics Interface Grammar Semantic Construction An Example The constraints for the NPs are built from the above by the rules (b8) and (b9): A 1 :@(X A2 r, X L1 r )  A 2 :@(X 11 r, X 121 r )  L 1 :lam(X L2 r )  X 1 r :var  X L2 r ⊲ *X 1 r  (X 1 r )=X L1 r  X L1 r ≠X 1 r  X 1 s =X 11 s =X 121 s A 3 :@(X A4 r, X L3 r )  A 4 :@(X 221 r, X 2221 r )  L 3 :lam(X L4 r )  X 22 r :var  X L4 2 ⊲ *X 22 r  (X 22 r )=X L3 r  X L3 r ≠X 22 r  X 22 s =X 221 s =X 2221 s Then rule (b3) combines the transitive verb and its object X 2 r :@(X 21 r, X 22 r )  X 2 s =X 21 s =X 22 s The constraints for the NPs are built from the above by the rules (b8) and (b9): A 1 :@(X A2 r, X L1 r )  A 2 :@(X 11 r, X 121 r )  L 1 :lam(X L2 r )  X 1 r :var  X L2 r ⊲ *X 1 r  (X 1 r )=X L1 r  X L1 r ≠X 1 r  X 1 s =X 11 s =X 121 s A 3 :@(X A4 r, X L3 r )  A 4 :@(X 221 r, X 2221 r )  L 3 :lam(X L4 r )  X 22 r :var  X L4 2 ⊲ *X 22 r  (X 22 r )=X L3 r  X L3 r ≠X 22 r  X 22 s =X 221 s =X 2221 s Then rule (b3) combines the transitive verb and its object X 2 r :@(X 21 r, X 22 r )  X 2 s =X 21 s =X 22 s Computational Aspects Conclusion Computational Aspects Conclusion A2A2 A1A1 L1L1 L2L2

43. 19.01.200543 The Syntax-Semantics Interface Grammar Semantic Construction An Example The Syntax-Semantics Interface Grammar Semantic Construction An Example Rule (b1) analogously combines the subject and the VP X  r :@(X 2 r, X 1 r )  X  s =X 2 s =X 1 s So far we have the following constraint: X 11 r :every  X 121 r :linguist  X 21 r :attend  X 221 r :a  X 2221 r :workshop  A 1 :@(X A2 r, X L1 r )  A 2 :@(X 11 r, X 121 r )  L 1 :lam(X L2 r )  X 1 r :var  X L2 r ⊲ *X 1 r  (X 1 r )=X L1 r  X L1 r ≠X 1 r  A 3 :@(X A4 r, X L3 r )  A 4 :@(X 221 r, X 2221 r )  L 3 :lam(X L4 r )  X 22 r :var  X L4 2 ⊲ *X 22 r  (X 22 r )=X L3 r  X L3 r ≠X 22 r  X 2 r :@(X 21 r, X 22 r )  X  r :@(X 2 r, X 1 r )  X 1 s =X 11 s =X 121 s =X 22 s =X 221 s =X 2221 s =X 21 s =X  s =X 2 s Rule (b1) analogously combines the subject and the VP X  r :@(X 2 r, X 1 r )  X  s =X 2 s =X 1 s So far we have the following constraint: X 11 r :every  X 121 r :linguist  X 21 r :attend  X 221 r :a  X 2221 r :workshop  A 1 :@(X A2 r, X L1 r )  A 2 :@(X 11 r, X 121 r )  L 1 :lam(X L2 r )  X 1 r :var  X L2 r ⊲ *X 1 r  (X 1 r )=X L1 r  X L1 r ≠X 1 r  A 3 :@(X A4 r, X L3 r )  A 4 :@(X 221 r, X 2221 r )  L 3 :lam(X L4 r )  X 22 r :var  X L4 2 ⊲ *X 22 r  (X 22 r )=X L3 r  X L3 r ≠X 22 r  X 2 r :@(X 21 r, X 22 r )  X  r :@(X 2 r, X 1 r )  X 1 s =X 11 s =X 121 s =X 22 s =X 221 s =X 2221 s =X 21 s =X  s =X 2 s Computational Aspects Conclusion Computational Aspects Conclusion A4A4 A3A3 A2A2 A1A1 L4L4 L3L3 L2L2 L1L1 XrXr X2rX2r

44. 19.01.200544 The Syntax-Semantics Interface Grammar Semantic Construction An Example The Syntax-Semantics Interface Grammar Semantic Construction An Example Finally we add the relevant scope island constraints: The complete sentence is associated with the variable X  s, and all other X s variables are forced to be equal to this one by other constraints Node 11 is a determiner and node 21 is a verb; so we add the constraint X 11 s ⊲ * X 11 r  X 21 s ⊲ * X 21 r Finally we add the relevant scope island constraints: The complete sentence is associated with the variable X  s, and all other X s variables are forced to be equal to this one by other constraints Node 11 is a determiner and node 21 is a verb; so we add the constraint X 11 s ⊲ * X 11 r  X 21 s ⊲ * X 21 r Computational Aspects Conclusion Computational Aspects Conclusion

45. 19.01.200545 The Syntax-Semantics Interface Grammar Semantic Construction An Example The Syntax-Semantics Interface Grammar Semantic Construction An Example The final constraint we get is the following: X 11 r :every  X 121 r :linguist  X 21 r :attend  X 221 r :a  X 2221 r :workshop  A 1 :@(X A2 r, X L1 r )  A 2 :@(X 11 r, X 121 r )  L 1 :lam(X L2 r )  X 1 r :var  X L2 r ⊲ *X 1 r  (X 1 r )=X L1 r  X L1 r ≠X 1 r  A 3 :@(X A4 r, X L3 r )  A 4 :@(X 221 r, X 2221 r )  L 3 :lam(X L4 r )  X 22 r :var  X L4 2 ⊲ *X 22 r  (X 22 r )=X L3 r  X L3 r ≠X 22 r  X 2 r :@(X 21 r, X 22 r )  X  r :@(X 2 r, X 1 r )  X 1 s =X 11 s =X 121 s =X 22 s =X 221 s =X 2221 s =X 21 s =X  s =X 2 s  X  s ⊲ * X 11 r  X  s ⊲ * X 21 r The final constraint we get is the following: X 11 r :every  X 121 r :linguist  X 21 r :attend  X 221 r :a  X 2221 r :workshop  A 1 :@(X A2 r, X L1 r )  A 2 :@(X 11 r, X 121 r )  L 1 :lam(X L2 r )  X 1 r :var  X L2 r ⊲ *X 1 r  (X 1 r )=X L1 r  X L1 r ≠X 1 r  A 3 :@(X A4 r, X L3 r )  A 4 :@(X 221 r, X 2221 r )  L 3 :lam(X L4 r )  X 22 r :var  X L4 2 ⊲ *X 22 r  (X 22 r )=X L3 r  X L3 r ≠X 22 r  X 2 r :@(X 21 r, X 22 r )  X  r :@(X 2 r, X 1 r )  X 1 s =X 11 s =X 121 s =X 22 s =X 221 s =X 2221 s =X 21 s =X  s =X 2 s  X  s ⊲ * X 11 r  X  s ⊲ * X 21 r Computational Aspects Conclusion Computational Aspects Conclusion A4A4 A3A3 A2A2 A1A1 L4L4 L3L3 L2L2 L1L1 XrXr X2rX2r X 221 r X 2221 r X 121 r X 22 r X1rX1r

46. 19.01.200546 The Syntax-Semantics Interface Grammar Semantic Construction An Example The Syntax-Semantics Interface Grammar Semantic Construction An Example Disambiguation of arbitrary CLLS description is very complex: it has been shown that even CLLS without binding is equivalent to context unification, whose decidability is an open problem in theoretical computer science There are, however, semi-decision procedures which will eventually enumerate all solved forms of a constraint For the sublanguage of dominance constraints it was shown, that the satisfiability problem is decidable, but NP-complete Disambiguation of arbitrary CLLS description is very complex: it has been shown that even CLLS without binding is equivalent to context unification, whose decidability is an open problem in theoretical computer science There are, however, semi-decision procedures which will eventually enumerate all solved forms of a constraint For the sublanguage of dominance constraints it was shown, that the satisfiability problem is decidable, but NP-complete Computational Aspects Conclusion Computational Aspects Conclusion Computational Aspects

47. 19.01.200547 An implementation of a solver for dominance constraints can be obtained by employing constraint programming with finite sets. The constraints can be solved by always performing deterministic propagation steps to eliminate hopeless choices before making case distinctions. It can be shown that all dominance constraints that are needed for the linguistic application belong to a fragment called normal dominance constraints. Satisfiability of a normal constraint can be checked by a graph algorithm of polynomial runtime; each reading can be enumerated in polynomial time as well. However the graph algorithm is not a complete solver for all dominance constraints. An implementation of a solver for dominance constraints can be obtained by employing constraint programming with finite sets. The constraints can be solved by always performing deterministic propagation steps to eliminate hopeless choices before making case distinctions. It can be shown that all dominance constraints that are needed for the linguistic application belong to a fragment called normal dominance constraints. Satisfiability of a normal constraint can be checked by a graph algorithm of polynomial runtime; each reading can be enumerated in polynomial time as well. However the graph algorithm is not a complete solver for all dominance constraints. Conclusion Computational Aspects

48. 19.01.200548 Computational Aspects CLLS allows the representation of scope ambiguities, anaphora and ellipsis in simple underspecified structures that are transparent and suitable for processing. We have shown that CLLS correctly represents many notorious problems from the literature involving scope, anaphora, ellipses and their interactions. Furthermore CLLS can be used to model reinterpretation (meaning shift) of aspect and NPs in an underspecified way. Nevertheless the linguistic coverage of CLLS still has to be extended. Various more formal aspects can also be pursued in the future. CLLS allows the representation of scope ambiguities, anaphora and ellipsis in simple underspecified structures that are transparent and suitable for processing. We have shown that CLLS correctly represents many notorious problems from the literature involving scope, anaphora, ellipses and their interactions. Furthermore CLLS can be used to model reinterpretation (meaning shift) of aspect and NPs in an underspecified way. Nevertheless the linguistic coverage of CLLS still has to be extended. Various more formal aspects can also be pursued in the future. Conclusion

49. 19.01.200549 Thank you! Conclusion