Markus Egg, Alexander Koller, Joachim Niehren The Constraint Language for Lambda Structures

1
Markus Egg, Alexander Koller, Joachim NiehrenThe
Constraint Language for Lambda Structures

• Ventsislav Zhechev
• SfS, Universität Tübingen
• e-mail vzhechev_at_sfs.uni-tuebingen.de

2
Agenda

• Introduction
• Motivation
• Basic Terms

• Elements of CLLS
• ?-terms
• ?-structures
• Discussed Phenomena

• Introduction
• Motivation
• Basic Terms
• Elements of CLLS
• ?-terms
• ?-structures
• Discussed Phenomena

3
Agenda (continued)

• Introduction
• Motivation
• Basic Terms

• Elements of CLLS
• ?-terms
• ?-structures
• Discussed Phenomena

• Syntax and Semantics of CLLS
• Tree Structures
• ?-structures
• Dominance and Parallelism
• The CLLS
• Constraint Graphs

4
Agenda (continued)

• Introduction
• Motivation
• Basic Terms

• Elements of CLLS
• ?-terms
• ?-structures
• Discussed Phenomena

• Interaction of Quantifiers, Anaphora and Ellipsis
• Quantifier Parallelism
• Strict/Sloppy Ambiguities
• Nested Ellipses
• A Complex Interaction
• Antecedent-Contained Ellipsis

5
Agenda (continued)

• Introduction
• Motivation
• Basic Terms

• Elements of CLLS
• ?-terms
• ?-structures
• Discussed Phenomena

• The Syntax-Semantics Interface
• Grammar
• Semantic Construction
• An Example
• Computational Aspects
• Conclusion

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• Introduction
• Motivation
• Basic Terms

• Introduction
• Motivation
• Basic Terms

• Introduction
• Motivation
• Basic Terms

• Elements of CLLS
• ?-terms
• ?-structures
• Discussed Phenomena

• Linguistic Phenomena
• Scope Ambiguities
• Anaphora
• VP Ellipsis
• Underspecification

Introduction
Motivation
7

• Introduction
• Motivation
• Basic Terms

• Introduction
• Motivation
• Basic Terms

• Elements of CLLS
• ?-terms
• ?-structures
• Discussed Phenomena

• Trees
• Underspecification
• Constraint Language for Lambda StructuresA
  Combination of Constraints
• Dominance Constraints
• Anaphoric Binding Constraints
• Parallelism Constraints
• ?-binding Constraints

Basic Terms
8

• Introduction
• Motivation
• Basic Terms

• 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

• 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)
• lte,tgt ? one-place predicates
• lte,lte,tgtgt? two-place predicates
• etc.

Elements of CLLS
?-terms
9

• Elements of CLLS
• ?-terms
• ?-structures
• Discussed Phenomena

• Syntax and Semantics of CLLS
• Tree Structures
• ?-structures
• Dominance and Parallelism
• The CLLS
• Constraint Graphs

• Elements of CLLS
• ?-terms
• ?-structures
• Discussed Phenomena

• (a workshop)(?x (every linguist)(?y (attend x)
  y))
• lam ? ?-abstraction
• _at_ ? functional application
• var ? bound variable
• ? variable binding

?-structures
10

• Elements of CLLS
• ?-terms
• ?-structures
• Discussed Phenomena

• Syntax and Semantics of CLLS
• Tree Structures
• ?-structures
• Dominance and Parallelism
• The CLLS
• Constraint Graphs

• Elements of CLLS
• ?-terms
• ?-structures
• Discussed Phenomena

• Scope Ambiguity
• Every linguist attends a workshop.
• (a workshop)(?x (every linguist)(?y (atten
  d x) y))
• (every linguist)(?y (a workshop)(?x (atten
  d x) y))
• ? dominance

Discussed Phenomena
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• Elements of CLLS
• ?-terms
• ?-structures
• Discussed Phenomena

• Syntax and Semantics of CLLS
• Tree Structures
• ?-structures
• Dominance and Parallelism
• The CLLS
• Constraint Graphs

• VP Ellipsis
• Every man sleeps, and so does Mary.
• Parallelism ConstraintX1/X2Y1/Y2

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• Elements of CLLS
• ?-terms
• ?-structures
• Discussed Phenomena

• Syntax and Semantics of CLLS
• Tree Structures
• ?-structures
• Dominance and Parallelism
• The CLLS
• Constraint Graphs

• Anaphora
• Johni said heij liked hisj mother.
• ana ? anaphora
• ? anaphoric link

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• Elements of CLLS
• ?-terms
• ?-structures
• Discussed Phenomena

• Syntax and Semantics of CLLS
• Tree Structures
• ?-structures
• Dominance and Parallelism
• The CLLS
• Constraint Graphs

• 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

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• 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

• 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

• 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 fk 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
  ?1such that ???1

Syntax and Semantics of CLLS
Tree Structures
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• 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

• Tree Structures
• tree domain ? is a finite nonempty set of nodes,
  which is prefix closed (???? ? ???) and closed
  under left siblings (?i?? ? ?j?? for all 1jlti)
• tree structure is defined as follows
• Given nodes ?0,..., ?n, we write ?0f(?1,..., ?n)
  for(?0, ?1,..., ?n) ? f

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• 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

• Tree Structures and ?-structures
• Formalization
• For ?-structures we assumevar0, ana0, lam1,
  _at_2 ? ?
• We define ?-structures as follows
• We draw ?-structures as tree-like graphs

?-structures
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• 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

• 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 and Parallelism
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• 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

• Correspondence Functions between segments
• Parallelism Relation

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• 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

20

• 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
• ?-structures
• Dominance and Parallelism
• The CLLS
• Constraint Graphs

• Syntax and Semantics of CLLS
• Tree Structures
• ?-structures
• Dominance and Parallelism
• The CLLS
• Constraint Graphs

• We assume an infinite set of node variables,
  ranged over X, Xi, 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

The CLLS
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• 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

• 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

Constraint Graphs
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• 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

• 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

• Throughout the chapter we assume a fixed
  signature?_at_2, lam1, var0, ana0, before2,
  mary0, read0, ...
• 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
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• The Syntax-Semantics Interface
• Grammar
• Semantic Construction
• An Example
• Computational Aspects
• Conclusion

• 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

• 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

Quantifier Parallelism
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• The Syntax-Semantics Interface
• Grammar
• Semantic Construction
• An Example
• Computational Aspects
• Conclusion

• 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

• John likes his mother, and Bill does too.
• The sentence has two readings strict (Bill likes
  Johns mother) and sloppy (Bill likes Bills
  mother)
• We describe the meaning of the sentence using
  parallelism and anaphoric linking constraints

Strict/Sloppy Ambiguities
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• 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

• According to the parallelism constraint the tree
  part of the ?-structure below Xt is the same as
  the one below Xs, except for the contrasting
  elements, as follows
• This is yet not a complete ?-structure, because
  the anaphor at Xa doesnt have an antecedent

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• The Syntax-Semantics Interface
• Grammar
• Semantic Construction
• An Example
• Computational Aspects
• Conclusion

• 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

• 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

Nested Ellipses
27

• 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

• All five readings are represented by the
  following constraint

28

• The Syntax-Semantics Interface
• Grammar
• Semantic Construction
• An Example
• Computational Aspects
• Conclusion

• 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

• 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

A Complex Interaction
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• 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

• Schematic representations of the solutions
• First reading
• Second reading
• Third reading

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• The Syntax-Semantics Interface
• Grammar
• Semantic Construction
• An Example
• Computational Aspects
• Conclusion

• 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

• 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

Antecedent-Contained Ellipsis
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• 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

• There is one problem with this analysisthe
  notion of binding equivalence as defined is too
  strong a restriction for ACD
• The redefinition is given as

32

• 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 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.

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• 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
• Computational Aspects
• Conclusion

• Computational Aspects
• Conclusion

• 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
34

• The Syntax-Semantics Interface
• Grammar
• Semantic Construction
• An Example

• The Syntax-Semantics Interface
• Grammar
• Semantic Construction
• An Example

• Computational Aspects
• Conclusion

• 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
35

• The Syntax-Semantics Interface
• Grammar
• Semantic Construction
• An Example

• Computational Aspects
• Conclusion

• 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 Xi
• The variables associated with syntactic nodes are
  related by the following rules

36

• The Syntax-Semantics Interface
• Grammar
• Semantic Construction
• An Example

• Computational Aspects
• Conclusion

37

• The Syntax-Semantics Interface
• Grammar
• Semantic Construction
• An Example

• Computational Aspects
• Conclusion

38

• The Syntax-Semantics Interface
• Grammar
• Semantic Construction
• An Example

• Computational Aspects
• Conclusion

39

• The Syntax-Semantics Interface
• Grammar
• Semantic Construction
• An Example

• Computational Aspects
• Conclusion

• 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
  typeX?rsleep
• 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 constraintX?rXi, when we process ? and
  the constraint X?rana ?ante(X?r)Xi when we
  process ?

40

• The Syntax-Semantics Interface
• Grammar
• Semantic Construction
• An Example

• Computational Aspects
• Conclusion

• The constraint for a relative pronoun with index
  i at ? isX?rXi ? Xivar and the constraint for
  the corresponding trace (say, at ?) is X?rXi.
  This, together with rule (b11), enforces correct
  binding of the trace
• The constraints for possessive pronouns, such as
  his, are as follows

41

• The Syntax-Semantics Interface
• Grammar
• Semantic Construction
• An Example

• The Syntax-Semantics Interface
• Grammar
• Semantic Construction
• An Example

• Computational Aspects
• Conclusion

• Every linguist attends a workshop.
• First the lexical elements introduce several
  labeling constraintsX11revery, X121rlinguist,
  X21rattend,X221ra, X2221rworkshop

An Example
42

• The Syntax-Semantics Interface
• Grammar
• Semantic Construction
• An Example

• Computational Aspects
• Conclusion

• The constraints for the NPs are built from the
  above by the rules (b8) and (b9)
• A1_at_(XA2r, XL1r) ? A2_at_(X11r, X121r) ?
  L1lam(XL2r) ?X1rvar ? XL2r?X1r ? ?(X1r)XL1r
  ? XL1r?X1r ? X1sX11sX121s
• A3_at_(XA4r, XL3r) ? A4_at_(X221r, X2221r) ?
  L3lam(XL4r) ?X22rvar ? XL42?X22r ?
  ?(X22r)XL3r ? XL3r?X22r ?X22sX221sX2221s
• Then rule (b3) combines the transitive verb and
  its object
• X2r_at_(X21r, X22r) ? X2sX21sX22s

43

• The Syntax-Semantics Interface
• Grammar
• Semantic Construction
• An Example

• Computational Aspects
• Conclusion

• Rule (b1) analogously combines the subject and
  the VP
• X?r_at_(X2r, X1r) ? X?sX2sX1s
• So far we have the following constraint
• X11revery ? X121rlinguist ? X21rattend ?
  X221ra ?X2221rworkshop ? A1_at_(XA2r, XL1r) ?
  A2_at_(X11r, X121r) ?L1lam(XL2r) ? X1rvar ?
  XL2r?X1r ? ?(X1r)XL1r ? XL1r?X1r ?A3_at_(XA4r,
  XL3r) ? A4_at_(X221r, X2221r) ? L3lam(XL4r) ?
  X22rvar ?XL42?X22r ? ?(X22r)XL3r ? XL3r?X22r
  ? X2r_at_(X21r, X22r) ?X?r_at_(X2r, X1r) ?
  X1sX11sX121sX22sX221sX2221sX21sX?sX2s

44

• The Syntax-Semantics Interface
• Grammar
• Semantic Construction
• An Example

• Computational Aspects
• Conclusion

• Finally we add the relevant scope island
  constraints
• The complete sentence is associated with the
  variable X?s, and all other Xs 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 X11s ? X11r ? X21s ? X21r

45

• The Syntax-Semantics Interface
• Grammar
• Semantic Construction
• An Example

• Computational Aspects
• Conclusion

• The final constraint we get is the following
• X11revery ? X121rlinguist ? X21rattend ?
  X221ra ?X2221rworkshop ? A1_at_(XA2r, XL1r) ?
  A2_at_(X11r, X121r) ?L1lam(XL2r) ? X1rvar ?
  XL2r?X1r ? ?(X1r)XL1r ? XL1r?X1r ?A3_at_(XA4r,
  XL3r) ? A4_at_(X221r, X2221r) ? L3lam(XL4r) ?
  X22rvar ?XL42?X22r ? ?(X22r)XL3r ? XL3r?X22r
  ? X2r_at_(X21r, X22r) ?X?r_at_(X2r, X1r) ?
  X1sX11sX121sX22sX221sX2221sX21sX?sX2s
  ?X?s ? X11r ? X?s ? X21r

46

• The Syntax-Semantics Interface
• Grammar
• Semantic Construction
• An Example

• Computational Aspects
• Conclusion

• Conclusion

• Computational Aspects

• 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
47

• Conclusion

• Computational Aspects

• 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.

48

• Computational Aspects

• Conclusion

• Conclusion

• 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

• Conclusion

Thank you!