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 89
Page 8
... theorem of Heyting's intuitionistic propositional calculus 15 is derivable in his system, adding that “presumably ... theorems, and are also said to be Λ-provable. A logic is called normal if it includes Gödel's second axiom, which is ...
... theorem of Heyting's intuitionistic propositional calculus 15 is derivable in his system, adding that “presumably ... theorems, and are also said to be Λ-provable. A logic is called normal if it includes Gödel's second axiom, which is ...
Page 9
... theorems of the form Pα, and in place of Necessitation they have the rule from α → β infer Pα → Pβ. Lemmon suggests ... theorem of the logic, then it is falsified by some finite model which satisfies the logic. This property was dubbed ...
... theorems of the form Pα, and in place of Necessitation they have the rule from α → β infer Pα → Pβ. Lemmon suggests ... theorem of the logic, then it is falsified by some finite model which satisfies the logic. This property was dubbed ...
Page 10
... theorems of Λ. McKinsey actually showed something stronger: the size of a falsifying model for a non-theorem α is bounded above by a number that depends computably on the size of α. Thus to decide if α is a theorem it suffices to ...
... theorems of Λ. McKinsey actually showed something stronger: the size of a falsifying model for a non-theorem α is bounded above by a number that depends computably on the size of α. Thus to decide if α is a theorem it suffices to ...
Page 11
... theorem whenever α and β are, putting all theorems into the same equivalence class. This is a fact that applies to any logic that has the rule of Necessitation, and it allows algebraic models for normal logics to be confined to those ...
... theorem whenever α and β are, putting all theorems into the same equivalence class. This is a fact that applies to any logic that has the rule of Necessitation, and it allows algebraic models for normal logics to be confined to those ...
Page 13
... , 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 S4-theorem, then Mathematical Modal Logic: A View of its Evolution 13.
... , 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 S4-theorem, then Mathematical Modal Logic: A View of its Evolution 13.
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 |