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 60
Page 27
... logic of necessity and possibility, as distinct from tense logic. The l-calculus was intended to describe a very specific situation: an ordered system of dates or moments in time that forms an “infinite and continuous linear series ...
... logic of necessity and possibility, as distinct from tense logic. The l-calculus was intended to describe a very specific situation: an ordered system of dates or moments in time that forms an “infinite and continuous linear series ...
Page 36
... logic, ranging across the foundations of constructive logic and set theory, substructural logics (including relevance logic, linear logic), provability logic, the Kripke-Joyal semantics in topos theory and numerous logics of transition ...
... logic, ranging across the foundations of constructive logic and set theory, substructural logics (including relevance logic, linear logic), provability logic, the Kripke-Joyal semantics in topos theory and numerous logics of transition ...
Page 41
... logic of integer time does not.42 This is not quite the end of the story about Diodorean modality. Prior made an interesting observation in [Prior, 1967, p. 203] about the (non-linear) temporal ordering of locations in relativistic ...
... logic of integer time does not.42 This is not quite the end of the story about Diodorean modality. Prior made an interesting observation in [Prior, 1967, p. 203] about the (non-linear) temporal ordering of locations in relativistic ...
Page 43
... logic K4W,46 with axioms 4 : Pp → PPp W : P(Pp → p) → Pp, is characterised by the class of finite frames (K, R) in which R is transitive and irreflexive, i.e. a strict ordering. (This logic ... linear orderings (both irreflexive and ...
... logic K4W,46 with axioms 4 : Pp → PPp W : P(Pp → p) → Pp, is characterised by the class of finite frames (K, R) in which R is transitive and irreflexive, i.e. a strict ordering. (This logic ... linear orderings (both irreflexive and ...
Page 46
... logic is characterised by some class of relational frames [Lemmon, 1977, p ... logic was devised by Steven Thomason [1972b], and is a readily described tense ... linear ordering with no last element. Interpreting p as a set such that both ...
... logic is characterised by some class of relational frames [Lemmon, 1977, p ... logic was devised by Steven Thomason [1972b], and is a readily described tense ... linear ordering with no last element. Interpreting p as a set such that both ...
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 |