The Semantics and Proof Theory of the Logic of Bunched Implications

David J. Pym

ISBN 10: 1402007450 / ISBN 13: 9781402007453

Editore: Springer Netherlands, Springer Netherlands, 2002

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Druck auf Anfrage Neuware - Printed after ordering - This is a monograph about logic. Specifically, it presents the mathe matical theory of the logic of bunched implications, BI: I consider Bl's proof theory, model theory and computation theory. However, the mono graph is also about informatics in a sense which I explain. Specifically, it is about mathematical models of resources and logics for reasoning about resources. I begin with an introduction which presents my (background) view of logic from the point of view of informatics, paying particular attention to three logical topics which have arisen from the development of logic within informatics: - Resources as a basis for semantics; - Proof-search as a basis for reasoning; and - The theory of representation of object-logics in a meta-logic. The ensuing development represents a logical theory which draws upon the mathematical, philosophical and computational aspects of logic. Part I presents the logical theory of propositional BI, together with a computational interpretation. Part II presents a corresponding devel opment for predicate BI. In both parts, I develop proof-, model- and type-theoretic analyses. I also provide semantically-motivated compu tational perspectives, so beginning a mathematical theory of resources. I have not included any analysis, beyond conjecture, of properties such as decidability, finite models, games or complexity. I prefer to leave these matters to other occasions, perhaps in broader contexts.

Codice articolo 9781402007453

Dati bibliografici

• Titolo: The Semantics and Proof Theory of the Logic of Bunched Implications
• Editore: Springer Netherlands, Springer Netherlands
• Data di pubblicazione: 2002
• Lingua: Inglese
• ISBN 10: 1402007450
• ISBN 13: 9781402007453
• Rilegatura: Buch
• Condizione: Neu
• Dimensioni: 241 L x 160 A x 24 P (millimetri) 241 millimetri di larghezza per 160 millimetri di altezza per 24 millimetri di profondità
• Peso: 682 grammi

Descrizione articolo

Riassunto

This is a monograph about logic. Specifically, it presents the mathe­ matical theory of the logic of bunched implications, BI: I consider Bl's proof theory, model theory and computation theory. However, the mono­ graph is also about informatics in a sense which I explain. Specifically, it is about mathematical models of resources and logics for reasoning about resources. I begin with an introduction which presents my (background) view of logic from the point of view of informatics, paying particular attention to three logical topics which have arisen from the development of logic within informatics: Resources as a basis for semantics; Proof-search as a basis for reasoning; and The theory of representation of object-logics in a meta-logic. The ensuing development represents a logical theory which draws upon the mathematical, philosophical and computational aspects of logic. Part I presents the logical theory of propositional BI, together with a computational interpretation. Part II presents a corresponding devel­ opment for predicate BI. In both parts, I develop proof-, model- and type-theoretic analyses. I also provide semantically-motivated compu­ tational perspectives, so beginning a mathematical theory of resources. I have not included any analysis, beyond conjecture, of properties such as decidability, finite models, games or complexity. I prefer to leave these matters to other occasions, perhaps in broader contexts.

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)