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The Ontology of Language

Properties, Individuals and Discourse

How can the meaning of language be represented by formal logic? Similar research regarding the semantics of natural language has suggested that standard, ’classical’ logical systems must be extended to account for the meaning of pronouns and other nominal expressions. But Chris Fox argues that by reconsidering how natural language in a formal logic is represented, the extension of classical logical systems is not required.

The Ontology of Language explores how semantic issues can be addressed in a way that minimizes the ontological commitments of the resulting semantics. The book works within a version of Property Theory stemming from a combination of the lambda calculus with Aczel’s Frege structures-a combination originally developed by Raymond Turner. Fox then improves on this version and substantially extends it with original applications to plurals and mass nouns, to ’intensional individuals’, and to the dynamics of discourse. Some useful appendixes on further extensions and alternatives are included.

192 pages | 6 x 9 | © 2000

Lecture Notes

Language and Linguistics: General Language and Linguistics

Table of Contents

1. Introduction
1.1 Individuals, Properties and Guises
1.2 The Methodology of Least Commitment
1.3 Plurals and Mass Terms
1.4 Discourse Representation
1.5 Summary
2. Property Theory
2.1 Motivation
2.2 PT: An Axiomatic Property Theory
2.3 Definitions of Types
2.4 The Paradoxes as a Category Mistake
2.5 Internal Definability
2.6 Model
2.7 Syntax-Semantics Interface
2.8 PTQ-like interpretation
2.9 Other Approaches
3. Plurals and Mass Terms
3.1 Plurals
3.2 Mass Terms
3.3 A Unification
3.4 A Model of PT with Boolean Terms
3.5 Conclusions
4. Roles and Guises
4.1 Intensional Individuals
4.2 Landman’s Formal Theory
4.3 Roles in PT
4.4 Property Modifiers
4.5 Appropriate Guises
4.6 Semantics with Property Modifiers
4.7 The Behaviour of Property Modifiers
4.8 Conclusions
5. Discourse Representation
5.1 Discourse in Classical Logic
5.2 Discourse in Property Theory
5.3 A Sketch of the Basic Theory
5.4 PT^dt: PT with Discourse Terms
5.5 Relative Clauses
5.6 Summary
5.7 Consistency of PT^dt
5.8 Conclusions
6. Conclusions
6.1 Properties
6.2 Individuals
6.3 Discourse
6.4 The Methodology of Least Commitment
A. Dynamic Property Theory
B. Dependent Types AND Discourse
C. Semantics of NL in PT^dt
C.1 Examples
D. Negation AND Disjunction in Discourse
D.1 Negation of Classical Propositions
D.2 Negation of Types
D.3 Double Negation and Disjunction
D.4 Proper Nouns and Negation
D.5 Axioms for negation in PT^dt
Author Index
Formal Index
General Index

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