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 2
... first version as a “perplexing open question”. This was the question of whether a logic validated by its canonical frame must be characterised by a first-order definable class of frames. Also, a new section 7.7 has been added to ...
... first version as a “perplexing open question”. This was the question of whether a logic validated by its canonical frame must be characterised by a first-order definable class of frames. Also, a new section 7.7 has been added to ...
Page 14
... first-order logic. 3.3 BAO's: The Theory of Jónsson and Tarski The notion. 19In the technical algebraic sense of having no non-trivial congruences. 20This was answered negatively by Lyndon [1950]. Work of Tarski, 14 Robert Goldblatt.
... first-order logic. 3.3 BAO's: The Theory of Jónsson and Tarski The notion. 19In the technical algebraic sense of having no non-trivial congruences. 20This was answered negatively by Lyndon [1950]. Work of Tarski, 14 Robert Goldblatt.
Page 23
... order quantificational S5, and a complete axiomatisation of it using a ... order logic, and Bayart commented [1959, p. 100] that he had just adapted Henkin's ... first argument, and having individuals as the remaining arguments when n =0 ...
... order quantificational S5, and a complete axiomatisation of it using a ... order logic, and Bayart commented [1959, p. 100] that he had just adapted Henkin's ... first argument, and having individuals as the remaining arguments when n =0 ...
Page 24
... first order fragment of the system is complete for validity in all universes. The method used was subsequently generalised in [Cresswell, 1967] to obtain a completeness theorem for the relational semantics of a first order version of ...
... first order fragment of the system is complete for validity in all universes. The method used was subsequently generalised in [Cresswell, 1967] to obtain a completeness theorem for the relational semantics of a first order version of ...
Page 25
... first-order language of a binary predicate symbol U, beginning with the following definitions, in which L and M are connectives for necessity and possibility (but the other notation is that of this paper rather than the original Polish): ...
... first-order language of a binary predicate symbol U, beginning with the following definitions, in which L and M are connectives for necessity and possibility (but the other notation is that of this paper rather than the original Polish): ...
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 |