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 92
Page 9
... finite model which satisfies the logic. This property was dubbed the finite model property by Ronald Harrop [1958], who proved the general result that any finitely axiomatisable propositional logic Λ with the finite model property is ...
... finite model which satisfies the logic. This property was dubbed the finite model property by Ronald Harrop [1958], who proved the general result that any finitely axiomatisable propositional logic Λ with the finite model property is ...
Page 10
... finite model which satisfies the axioms of Λ. By the finite model property this is just a listing of all the non-theorems of Λ. McKinsey actually showed something stronger: the size of a falsifying model for a non-theorem α is bounded ...
... finite model which satisfies the axioms of Λ. By the finite model property this is just a listing of all the non-theorems of Λ. McKinsey actually showed something stronger: the size of a falsifying model for a non-theorem α is bounded ...
Page 11
... finite S2-matrix in which the original falsifying evaluation of α can be reproduced. This same construction shows that S4 has the finite model property, with the minor simplification that the element ∗0 does not have to be worried ...
... finite S2-matrix in which the original falsifying evaluation of α can be reproduced. This same construction shows that S4 has the finite model property, with the minor simplification that the element ∗0 does not have to be worried ...
Page 12
... finite normal S4-matrix can be represented as the closure algebra of all subsets of some topological space, using the representation of a finite Boolean algebra as the powerset algebra of its set of atoms. McKinsey and Tarski now ...
... finite normal S4-matrix can be represented as the closure algebra of all subsets of some topological space, using the representation of a finite Boolean algebra as the powerset algebra of its set of atoms. McKinsey and Tarski now ...
Page 13
... (finite) closure algebras, as well as the closure algebra of any Euclidean space, or of any zero-dimensional dense-in-itself subspace of Euclidean space. Hence in view of result (5), the claim of [Gödel, 1933] follows: if Pα ∨ Pβ is an ...
... (finite) closure algebras, as well as the closure algebra of any Euclidean space, or of any zero-dimensional dense-in-itself subspace of Euclidean space. Hence in view of result (5), the claim of [Gödel, 1933] follows: if Pα ∨ Pβ is an ...
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 |