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 88
Page 4
Dov M. Gabbay, John Woods. The standard syntax for propositional modal logic is based on a countably infinite list p0 ,p1 ,... of propositional variables, for which we typically use the letters p,q,r. Formulas are generated from these ...
Dov M. Gabbay, John Woods. The standard syntax for propositional modal logic is based on a countably infinite list p0 ,p1 ,... of propositional variables, for which we typically use the letters p,q,r. Formulas are generated from these ...
Page 7
... propositional variables, and the following rules of inference. • Uniform substitution of formulas for propositional variables. • Substitution of strict equivalents: from (α = β) and γ infer any formula obtained from γ by substituting β ...
... propositional variables, and the following rules of inference. • Uniform substitution of formulas for propositional variables. • Substitution of strict equivalents: from (α = β) and γ infer any formula obtained from γ by substituting β ...
Page 8
... propositional calculus. That approach was first used in the note “An interpretation of the intuitionistic propositional calculus” [Gödel, 1933], published in the proceedings of Karl Menger's mathematical colloquium at the University of ...
... propositional calculus. That approach was first used in the note “An interpretation of the intuitionistic propositional calculus” [Gödel, 1933], published in the proceedings of Karl Menger's mathematical colloquium at the University of ...
Page 9
... logic obtained by adding the axiom p → PQp to Gödel's axiomatisation of S4. Following [Becker, 1930], p → PQp is called the Brouwerian axiom. The smallest normal logic ... propositional logic began as algebra, in the thought of Boole. We ...
... logic obtained by adding the axiom p → PQp to Gödel's axiomatisation of S4. Following [Becker, 1930], p → PQp is called the Brouwerian axiom. The smallest normal logic ... propositional logic began as algebra, in the thought of Boole. We ...
Page 10
... propositional logics and prove the independence of axioms. Their use as a general method for constructing logical systems is due to Alfred Tarski.17 A logic is characterised by a matrix if the matrix satisfies the theorems of the logic ...
... propositional logics and prove the independence of axioms. Their use as a general method for constructing logical systems is due to Alfred Tarski.17 A logic is characterised by a matrix if the matrix satisfies the theorems of the logic ...
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 |