somewhat like Henkin's nonstandard interpretation of higher-order logics, while the right semantics [or logical modalities is an analogue to the standard of type theory in Henkin's sense. interpretation Another possibility would be to follow W.V. Quine's advice to give up logi­ cal modalities as being beyond repair. Or we could also try to develop a logic of conceptual possibility, restricting the range of our "possible worlds" to those compatible with the transcendental presuppositions of our own conceptual sys­ tem. This looks (...) in fact like one of the most interesting possible theories I have dreamt of developing but undoubtedly never will. Its kinship with Kant's way of thinking should be obvious. Besides putting the entire enterprise of possible-worlds semantics into a perspective, we can also see that the actual history of possible-worlds seman­ tics is more complicated than it might first appear to be. For the standard in­ terpretation of modal logics has reared its beautiful head repeatedly in the writings of Stig Kanger, Richard Montague the pre-Montague-semantics theorist, and Nino Cocchiarella. (shrink)

Language in Action demonstrates the viability of mathematical research into the foundations of categorial grammar, a topic at the border between logic and linguistics. Since its initial publication it has become the classic work in the foundations of categorial grammar. A new introduction to this paperback edition updates the open research problems and records relevant results through pointers to the literature. Van Benthem presents the categorial processing of syntax and semantics as a central component in a more general dynamic logic (...) of information flow, in tune with computational developments in artificial intelligence and cognitive science. Using the paradigm of categorial grammar, he describes the substructural logics driving the dynamics of natural language syntax and semantics. This is a general type-theoretic approach that lends itself easily to proof-theoretic and semantic studies in tandem with standard logic. The emphasis is on a broad landscape of substructural categorial logics and their proof-theoretical and semantic peculiarities. This provides a systematic theory for natural language understanding, admitting of significant mathematical results. Moreover, the theory makes possible dynamic interpretations that view natural languages as programming formalisms for various cognitive activities. (shrink)

A comprehensive examination of the interfaces of logic, computer science, and game theory, drawing on twenty years of research on logic and games.

This book develops a view of logic as a theory of information-driven agency and intelligent interaction between many agents - with conversation, argumentation and games as guiding examples. It provides one uniform account of dynamic logics for acts of inference, observation, questions and communication, that can handle both update of knowledge and revision of beliefs. It then extends the dynamic style of analysis to include changing preferences and goals, temporal processes, group action and strategic interaction in games. Throughout, the book (...) develops a mathematical theory unifying all these systems, and positioning them at the interface of logic, philosophy, computer science and game theory. A series of further chapters explores repercussions of the 'dynamic stance' for these areas, as well as cognitive science. (shrink)

Reference and Existence, Saul Kripke's John Locke Lectures for 1973, can be read as a sequel to his classic Naming and Necessity. It confronts important issues left open in that work -- among them, the semantics of proper names and natural kind terms as they occur in fiction and in myth; negative existential statements; the ontology of fiction and myth. In treating these questions, he makes a number of methodological observations that go beyond the framework of his earlier book -- (...) including the striking claim that fiction cannot provide a test for theories of reference and naming. In addition, these lectures provide a glimpse into the transition to the pragmatics of singular reference that dominated his influential paper, " Speaker's Reference and Semantic Reference " -- a paper that helped reorient linguistic and philosophical semantics. Some of the themes have been worked out in later writings by other philosophers -- many influenced by typescripts of the lectures in circulation -- but none have approached the careful, systematic treatment provided here. The virtuosity of Naming and Necessity -- the colloquial ease of the tone, the dazzling, on-the-spot formulations, the logical structure of the overall view gradually emerging over the course of the lectures -- is on display here as well. (shrink)

Most current work in epistemology deals with the evaluation and justification of information already acquired. In this book, Jaakko Hintikka instead discusses the more important problem of how knowledge is acquired in the first place. His model of information-seeking is the old Socratic method of questioning, which has been generalized and brought up-to-date through the logical theory of questions and answers that he has developed. Hintikka also argues that philosophers' quest for a definition of knowledge is ill-conceived and that the (...) entire notion of knowledge should be replaced by the concept of information. He offers an analysis of the different meanings of the concept of information and of their interrelations. The result is a new and illuminating approach to the field of epistemology. (shrink)

In this paper we discuss the way logical consequence depends on what sets there are. We try to find out what set-theoretical assumptions have to be made to determine a logic, i.e., to give a definite answer to whether any given argument is correct. Consideration of second order logic -which is left highly indetermined by the usual set-theoretical axioms- prompts us to suggest a slightly different but natural nation of logical consequence, which reduces second order logic indeterminacy without interfering with (...) first order logic. (shrink)