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 81
Page 1
... notion of necessity, nor consequently of possibility. If this conclusion is valid, the subject of modality ought to be banished from logic, since propositions are simply true or false . . . [Russell, 1905] 1 INTRODUCTION Modal logic was ...
... notion of necessity, nor consequently of possibility. If this conclusion is valid, the subject of modality ought to be banished from logic, since propositions are simply true or false . . . [Russell, 1905] 1 INTRODUCTION Modal logic was ...
Page 8
... notion of a logic refers to any set Λ of formulas that includes all truth-functional tautologies and is closed under the rules of uniform substitution for variables and detachment for material implication. The formulas belonging to Λ ...
... notion of a logic refers to any set Λ of formulas that includes all truth-functional tautologies and is closed under the rules of uniform substitution for variables and detachment for material implication. The formulas belonging to Λ ...
Page 9
... notion of an abstract algebra was being pursued [Birkhoff, 1933; 1935]. Over the next few years, algebraic techniques were applied to the study of modal systems, using modal algebras: Boolean algebras with an additional operation to ...
... notion of an abstract algebra was being pursued [Birkhoff, 1933; 1935]. Over the next few years, algebraic techniques were applied to the study of modal systems, using modal algebras: Boolean algebras with an additional operation to ...
Page 15
... notion of a Boolean algebra with operators (BAO) was introduced by Jónsson and Tarski in their abstract [1948], with the details of their announced results being presented in [1951]. That work contains representations of algebras that ...
... notion of a Boolean algebra with operators (BAO) was introduced by Jónsson and Tarski in their abstract [1948], with the details of their announced results being presented in [1951]. That work contains representations of algebras that ...
Page 19
... notion of “S5-tautology” precisely characterises the theorems of propositional S5, a result that Kripke had in fact obtained first, before, as he explained in [1959a, fn. 4], aquaintance with Beth's paper led me to generalize the truth ...
... notion of “S5-tautology” precisely characterises the theorems of propositional S5, a result that Kripke had in fact obtained first, before, as he explained in [1959a, fn. 4], aquaintance with Beth's paper led me to generalize the truth ...
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 |