Ebook: Logic, language, and meaning vol.2: Intensional logic and logical grammar

Chapter 1 provides a background to the systems of intensional logic presented in chapters 2 and 3. The nature and limits of the semantics of predicate logic. are discussed, and Frege's attempts to develop an intensional theory of meaning are sketched.

Chapter 2 is concerned with the propositional part of intensional logic.A general characterization of possible-worlds semantics is given, and it is then demonstrated with reference to modal propositional logic and propositional tense logic. Attention is paid not only to logical and philosophical matters but also to potential applications in the analysis of natural language.


The same applies to the treatment of intensional predicate logic given in chapter 3, which appears here almost exclusively as a modal predicate logic. Different alternative semantic options are compared. Matters like rigid designation are discussed, along with certain more general methodological questions which come up in connection with intensional logic.

Chapter 4 introduces and compares the theory of types and categorial grammar. One important reason for preferring type-theoretical languages is the syntactic and semantic diversity of natural language. Increasing the applicability of logical systems in the systematic analysis of natural language is also the most important reason for introducing X-abstraction. Anticipating the discussion of Montague grammar in chapter 6, certain methodological requirements are discussed which must be met in such an application, together with the role which X-abstraction can play in helping to meet these requirements. Chapter 4 also contains an exposition of the principles of categorial grammar.

In chapter 5, intensional logic and the theory of types are combined. The resulting intensional theory of types is the logical system exploited in Montague grammar in order to provide a logical semantics for (a fragment of) a natural language. A section on two-sorted type theory has been included in order to render certain formal properties of the intensional theory of types more comprehensible.

Chapter 6 begins with a discussion of a number of the assumptions made when systematically applying logical systems in the semantic analysis of natural language. This is followed by an exposition of the best-known model of logical grammar, viz., Montague grammar. The form and function of Montague grammar are demonstrated in detail with reference to the syntax and semantics of a fragment of English.

Chapter 7 is a survey of three recent developments in model-theoretic semantics of natural language. The first of these is the theory of generalized quantifiers which has been developed in the late seventies and which builds on the analysis of quantified expressions that can be found in Montague grammar. This development is particularly interesting because it brings logical grammar within the realm of empirical constraints. Next, some attention is paid to recent attempts to make 'classical' categorial grammar into a better
tool for natural language description. The third subject is discourse representation theory, which was developed in the early eighties. This theory aims at improving logical grammar with respect to problems of anaphoric relations and at extending it to the level of discourse. Biographical notes and references to relevant literature conclude this volume, without any pretence at being exhaustive.