4 Constraint Solving

In this section we show how we can extract the semantic representations of the vraious readings of a sentence from its constraimt graph, how to actually implement constraints and an enumeration procedure, and how we can use our semantics construction framework to derive constraints from the syntactic analysis of an NL sentence.

From Constraints to Formulae: Now we know how to describe the possible readings of a scope ambiguity by means of a constraint graph. The next thing we need to find out is how we can extract the semantic representations of the readings from the graph. This is going to be the topic of the first part of this section. Later we will show you how to actually implement constraints and an enumeration procedure. Last not least, you will see how we can use our semantics construction framework to derive constraints from the syntactic analysis of an NL sentence.

• 4.1 Constraint Solving
  • 4.1.1 Satisfiability and Enumeration
  • 4.1.2 Solved Forms
  • 4.1.3 Solved Forms: An Example
  • 4.1.4 Defining Solved Forms

• 4.2 An Algorithm For Solving Constraints
  • 4.2.1 The Choice Rule
  • 4.2.2 Normalization
  • 4.2.3 The Enumeration Algorithm

• 4.3 Constraint Solving in Prolog
  • 4.3.1 Prolog Representation of Constraint Graphs
  • 4.3.2 Solve
  • 4.3.3 Distribute
  • 4.3.4 (Parent) Normalization
  • 4.3.5 Redundancy Elimination

• 4.4 Semantics Construction for Underspecified Semantics
  • 4.4.1 The Semantic Macros
    • The Simple Macros
    • Macros for the Determiners
  • 4.4.2 The combine-rules
    • 
    • 
    • Example: ``A woman walks''
    • , , and

• 4.5 Running CLLS