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Table of Contents
Table of Contents
Preface
1 Semantic Construction
1.1 Introduction
1.2 First-Order Logic: Basic Concepts
1.2.1 Vocabularies
1.2.2 First-Order Languages
1.2.3 Building Formulas
1.2.4 Bound and Free Variables
1.2.5 Notation
1.2.6 Representing formulas in Prolog
1.3 Building Meaning Representations
1.3.1 Being Systematic
1.3.2 Being Systematic (II)
1.3.3 Three Tasks
1.3.4 From Syntax to Semantics
1.4 The Lambda Calculus
1.4.1 Lambda-Abstraction
1.4.2 Reducing Complex Expressions
1.4.3 Using Lambdas
1.4.4 Advanced Topics: Proper Names and Transitive Verbs
1.4.5 The Moral
1.4.6 What's next
1.4.7 [Sidetrack:] Accidental Bindings
1.4.8 [Sidetrack:] Alpha-Conversion
1.5 Implementing Lambda Calculus
1.5.1 Representations
1.5.2 Extending the DCG
1.5.3 The Lexicon
1.5.4 A First Run
1.5.5 Beta-Conversion
1.5.6 Beta-Conversion Continued
1.5.7 Running the Program
2 Towards a Modular Architecture
2.1 Architecture of our Grammar
2.2 The Syntax Rules
2.2.1 Ideal Syntax Rules
2.2.2 The Syntax Rules we will use
2.3 The Semantic Side
2.3.1 The Semantically Annotated Syntax Rules
2.3.2 Implementing
combine/2
for Functional Application
2.4 Looking Up the Lexicon
2.4.1 Lexical Rules
2.4.2 The Lexicon
2.4.3 ``Special'' Words
2.4.4 Semantic Macros for Lambda-Calculus
2.5 Lambda at Work
3 Scope and Underspecification
3.1 Scope Ambiguities
3.1.1 What Are Scope Ambiguities?
3.1.2 Scope Ambiguities and Montague Semantics
3.1.3 A More Complex Example
3.1.4 The Fifth Reading
3.1.5 Montague's Approach to the Scope Problem
3.1.6 Quantifying In: An Example
3.1.7 Other Traditional Solutions
3.1.8 The Problem with the Traditional Approaches
3.2 Underspecification
3.2.1 Introduction
3.2.2 Computational Advantages
3.2.3 Underspecified Descriptions
3.2.4 The Masterplan
3.2.5 Formulas are trees!
3.2.6 Describing Lambda-Structures
3.2.7 From Lambda-Expressions to an Underspecified Description
3.2.8 Relating Constraint Graphs and Lambda-Structures
3.2.9 Sidetrack: Constraint Graphs - The True Story
3.2.10 Sidetrack: Predicates versus Functions
4 Constraint Solving
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
5 Inference in Computational Semantics
5.1 Basic Semantic Concepts
5.1.1 Models
5.1.2 An Example Model
5.1.3 Satisfaction, Assignments
5.1.4 Interpretations and Variant Assignments
5.1.5 The Satisfaction Definition
5.1.6 Truth in a Model
5.1.7 Validities
5.1.8 Valid Arguments
5.1.9 Calculi
5.2 Tableaux Calculi
5.2.1 Tableaux for Theorem Proving
5.2.2 Tableaux for Theorem Proving (continued)
5.2.3 Summing up
5.2.4 Using Tableaux to test Truth Conditions and Entailments
5.2.5 An Application: Conversational Maxims
5.2.6 The Maxim of Quality
5.2.7 The Maxim of Quantity
5.3 Tableaux Web-Interface
6 Tableaux Implemented
6.1 Implementing PLNQ
6.1.1 Literals
6.1.2 Complex Formulae: Negation
6.1.3 Complex Formulae: Conjunctive Expansion
6.1.4 Complex Formulae: Disjunctive Expansion
6.1.5 An Example - first Steps
6.1.6 An Example - final Step
6.1.7 Another Example
6.1.8 Two Connectives
6.2 Wrapping it up (Theorem Proving)
Bibliography
Index
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Aljoscha Burchardt
,
Alexander Koller
and
Stephan Walter
Version 1.2.5 (20030212)