The Semantics and Proof Theory of the Logic of Bunched Implications (Applied Logic Series)

David J. Pym

ISBN 10: 9048160723 / ISBN 13: 9789048160723

Editore: Springer, 2002

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338 pages. 9.25x6.10x0.77 inches. In Stock. Codice articolo x-9048160723

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Titolo: The Semantics and Proof Theory of the Logic ...

Casa editrice: Springer

Data di pubblicazione: 2002

Legatura: Paperback

Condizione: Brand New

Descrizione articolo

Riassunto:

This monograph provides a thorough account of the model theory, proof theory and computational interpretations of BI, the logic of bunched implications, which freely combines intuitionistic logic and multiplicative intuitionistic linear logic. Starting, on the one hand, from elementary observations about modelling resources and, on the other, from a desire to develop a system of logic within which additive (or extensional) and multiplicative (or intensional) implications co-exist with equal logical status, we give natural deduction, lambda-calculi, sequent calculus, categorical semantics, Kripke models, topological models, logical relations and computational interpretations for both propositional and predicate BI, within which both additive and multiplicative quantifiers also co-exist. This monograph will be of interest to graduate students and researchers in mathematical logic, philosophical logic, computational logic and theoretical computer science.

Recensione:

From the reviews:

"This monograph presents a mathematical theory of the logic of BI ... . Due to the author’s clear and approachable style this book may be interesting to a large circle of logicians, mathematicians and computer scientists. In particular, it could be useful to graduate students, specialists and researchers in the field of applications of logic in programming. In addition to its other qualities, this book also presents a significant contribution to a new area of mathematical logic―fibring logic ... .” (Branislav Boricic, Mathematical Reviews, Issue 2008 i)