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 69
Page 2
... 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 [Marx and Venema, 1997], for example). There ...
... 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 [Marx and Venema, 1997], for example). There ...
Page 14
... proof of the disjunction property for IPC: if α∨β is a theorem, then so is ... theory for S4 (see section 7.6). Another significant result of the 1948 ... Theory of Jónsson and Tarski The notion. 19In the technical algebraic sense of ...
... proof of the disjunction property for IPC: if α∨β is a theorem, then so is ... theory for S4 (see section 7.6). Another significant result of the 1948 ... Theory of Jónsson and Tarski The notion. 19In the technical algebraic sense of ...
Page 19
... proof employing the method of semantic tableaux introduced in [Beth, 1955]. It was then observed that for purely ... theory” and completeness theorems for a raft of modal systems, including S2–S5, the Feys–von Wright system T (or M) ...
... proof employing the method of semantic tableaux introduced in [Beth, 1955]. It was then observed that for purely ... theory” and completeness theorems for a raft of modal systems, including S2–S5, the Feys–von Wright system T (or M) ...
Page 20
... prove completeness theorems: a formula is true in all models iff it is a theorem of T; true in all transitive models ... theory is given by a new proof of the deduction rule in S4 that if Pα ∨ Pβ is deducible then so is one of α and β ...
... prove completeness theorems: a formula is true in all models iff it is a theorem of T; true in all transitive models ... theory is given by a new proof of the deduction rule in S4 that if Pα ∨ Pβ is deducible then so is one of α and β ...
Page 23
... theory that has been largely overlooked is the work of the Belgian logician ... theory a universe U is defined to be a disjoint pair A, B of sets, with ... proof is given. 24“En réalité notre exposé n'est qu'une adaptation du théor ...
... theory that has been largely overlooked is the work of the Belgian logician ... theory a universe U is defined to be a disjoint pair A, B of sets, with ... proof is given. 24“En réalité notre exposé n'est qu'une adaptation du théor ...
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 |