Logic and the Modalities in the Twentieth CenturyDov M. Gabbay, John Woods Elsevier, 2006 M05 10 - 732 pages Logic and the Modalities in the Twentieth Century is an indispensable research tool for anyone interested in the development of logic, including researchers, graduate and senior undergraduate students in logic, history of logic, mathematics, history of mathematics, computer science and artificial intelligence, linguistics, cognitive science, argumentation theory, philosophy, and the history of ideas. This volume is number seven in the eleven volume Handbook of the History of Logic. It concentrates on the development of modal logic in the 20th century, one of the most important undertakings in logic’s long history. Written by the leading researchers and scholars in the field, the volume explores the logics of necessity and possibility, knowledge and belief, obligation and permission, time, tense and change, relevance, and more. Both this volume and the Handbook as a whole are definitive reference tools for students and researchers in the history of logic, the history of philosophy, and any discipline, such as mathematics, computer science, artificial intelligence, for whom the historical background of his or her work is a salient consideration. · Detailed and comprehensive chapters covering the entire range of modal logic. · Contains the latest scholarly discoveries and interpretative insights that answer many questions in the field of logic. |
From inside the book
Results 1-5 of 65
Page 1
... predicate logic. The aim of this article is to review these developments in a way that provides some insight into how the present came to be as it is. The pervading theme is the mathematics underlying modal logic, and this has at least ...
... predicate logic. The aim of this article is to review these developments in a way that provides some insight into how the present came to be as it is. The pervading theme is the mathematics underlying modal logic, and this has at least ...
Page 2
... predicate logic is barely scratched, and proof theory is not discussed at all. I have not attempted to survey the work of the present younger generation of modal logicians (see [Chagrov and Zakharyaschev, 1997], [Kracht, 1999], and ...
... predicate logic is barely scratched, and proof theory is not discussed at all. I have not attempted to survey the work of the present younger generation of modal logicians (see [Chagrov and Zakharyaschev, 1997], [Kracht, 1999], and ...
Page 19
... predicate variables. A complete assignment for a formula α in a non-empty set D was defined to be any function that assigns an element of D to each free individual variable in α, a subset of Dn to each n-ary predicate variable occurring ...
... predicate variables. A complete assignment for a formula α in a non-empty set D was defined to be any function that assigns an element of D to each free individual variable in α, a subset of Dn to each n-ary predicate variable occurring ...
Page 22
... predicate letter and each ) : H ∈ K} of individuals that exist in any world. Axioms are given for quantificational versions of the basic modal logics and it is stated that the completeness theorems of [1963a] can be extended to them ...
... predicate letter and each ) : H ∈ K} of individuals that exist in any world. Axioms are given for quantificational versions of the basic modal logics and it is stated that the completeness theorems of [1963a] can be extended to them ...
Page 23
... predicate variables. This idea had been introduced in [Henkin, 1950] to give a completeness result for non-modal higher order logic, and Bayart commented [1959, p. 100] that he had just adapted Henkin's theorem to S5.24 The other source ...
... predicate variables. This idea had been introduced in [Henkin, 1950] to give a completeness result for non-modal higher order logic, and Bayart commented [1959, p. 100] that he had just adapted Henkin's theorem to S5.24 The other source ...
Contents
1 | |
Epistemic Logic Paul Gochet and Pascal Gribomont | 99 |
Deontic Logic Paul McNamara | 197 |
Relevant and Substructural Logics Greg Restall | 289 |
A N Priors Logic Peter Øhrstrøm and Per F V Hasle | 399 |
The Philosophical Background Peter Øhrstrøm and Per F V Hasle | 447 |
Common terms and phrases
½ ½ A.N. Prior accessibility relation agent algebra axiom axiomatisation belief Belnap Benthem bisimulation Boolean calculus characterised classical coalgebra complete Computer Science conjunction construction context defined definition deontic logic described situation disjunction doxastic doxastic logic dynamic logic entailment epistemic logic equivalent example expresses fact finite first-order formal formula frame function Gabbay Goldblatt Hintikka implication infon instance interpretation intuitionistic intuitionistic logic Journal of Symbolic Kripke language lattice linear logic Lorenzen means Meyer modal logic negation notion Ô Õ Ô obligations obligatory ÔÕ operator Philosophical Logic possible worlds predicate problem programs proof theory propositional content propositional logic provable quantifier relevant logic result satisfies Segerberg semantics sentence situation semantics statement structural rules substructural logics Symbolic Logic Tarski temporal logic tense logic theorem true truth utterance valid variables
References to this book
Lectures on the Curry-Howard Isomorphism, Volume 10 Morten Heine Sørensen,Paweł Urzyczyn No preview available - 2006 |