Book contents
- Frontmatter
- Contents
- Preface
- Symbols and notational conventions
- 1 Logic for linguists
- 2 Set theory
- 3 Inference and logical analysis of sentences
- 4 Propositional logic
- 5 Predicate logic
- 6 Deduction
- 7 Modal logic
- 8 Intensional logic and categorial grammar
- 9 Further extensions
- 10 Logic for linguists?
- References
- Answers to exercises
- Index
8 - Intensional logic and categorial grammar
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- Preface
- Symbols and notational conventions
- 1 Logic for linguists
- 2 Set theory
- 3 Inference and logical analysis of sentences
- 4 Propositional logic
- 5 Predicate logic
- 6 Deduction
- 7 Modal logic
- 8 Intensional logic and categorial grammar
- 9 Further extensions
- 10 Logic for linguists?
- References
- Answers to exercises
- Index
Summary
Intensions and extensions
In previous chapters we have shown how logical analysis parallels linguistic analysis. In this chapter we will attempt to integrate them into one theory.
In predicate logic, we gave meaning to linguistic expressions by correlating our language to a model in which extensions were assigned to individual constants and predicate constants, that is, single objects to individuals and sets of objects to predicates. In other words, providing a semantics for a language was taken to involve providing an account of which objects in the world individual terms and predicate terms should be taken to refer to. By doing this, we were, as a second step, able to formulate truth-conditions for the sentences of predicate logic. This, in turn, enabled us to characterize a notion of logical consequence for predicate logic and thereby to capture the kind of logical inferences that are possible in predicate logic. But many of the types of reasoning we normally engage in cannot be captured in the simple type of predicate logic we described in chapter 5. We have already discussed the addition of modal operators, and there is more to come. One of the things which were inadequate and oversimplified in our version of predicate logic was the conception of semantics as a simple pairing of linguistic expressions and objects in the world.
- Type
- Chapter
- Information
- Logic in Linguistics , pp. 125 - 147Publisher: Cambridge University PressPrint publication year: 1977