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 5
... definition of the class of formulas dealt with nor an axiomatisation of operations in the sense of a rigorous ... defined five different ones, S1–S5, in Appendix II of the book Symbolic Logic [1932] that he wrote with C. H. Langford ...
... definition of the class of formulas dealt with nor an axiomatisation of operations in the sense of a rigorous ... defined five different ones, S1–S5, in Appendix II of the book Symbolic Logic [1932] that he wrote with C. H. Langford ...
Page 6
... define strict implication. This later became the system S3 of [Lewis and Langford, 1932], which introduced instead ... defined with negation, conjunction, and possibility as their primitive connectives, but he made no use of a symbol for ...
... define strict implication. This later became the system S3 of [Lewis and Langford, 1932], which introduced instead ... defined with negation, conjunction, and possibility as their primitive connectives, but he made no use of a symbol for ...
Page 11
... define K1 such that ∗ 1 x = ∗x whenever x and ∗x are both in K1: an operation ∗ 1 on ∗1 x = n {∗y ∈ K1 : x ... defined to mean that 1∞ ≤ x, and it was shown that ⊣ x holds whenever x is any evaluation of a theorem of S2. In ...
... define K1 such that ∗ 1 x = ∗x whenever x and ∗x are both in K1: an operation ∗ 1 on ∗1 x = n {∗y ∈ K1 : x ... defined to mean that 1∞ ≤ x, and it was shown that ⊣ x holds whenever x is any evaluation of a theorem of S2. In ...
Page 13
... definition of certain Brouwerian algebras of the , 1), and a proof that every Brouwerian algebra is isomorphic to a ... defined ∨ is interpreted by x÷y = y. as x; and ¬ is interpreted as the unary operation x ÷ 1 = Θx. The algebra of ...
... definition of certain Brouwerian algebras of the , 1), and a proof that every Brouwerian algebra is isomorphic to a ... defined ∨ is interpreted by x÷y = y. as x; and ¬ is interpreted as the unary operation x ÷ 1 = Θx. The algebra of ...
Page 18
... definition of a relation algebra as an abstract BAO (3, ; , ̆, 1') that forms an involuted monoid under ; , ̆,1' and satifies the condition x ̆;−(x;y) ≤ −y. Concrete examples include the set P(S×S) of all binary relations on a set S ...
... definition of a relation algebra as an abstract BAO (3, ; , ̆, 1') that forms an involuted monoid under ; , ̆,1' and satifies the condition x ̆;−(x;y) ≤ −y. Concrete examples include the set P(S×S) of all binary relations on a set S ...
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 |