Del 26 i serien Applied Logic Series

Semantics and Proof Theory of the Logic of Bunched Implications

Inbunden, Engelska, 2002

AvDavid J. Pym

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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 intentional) implications co-exist with equal logical status, the book gives natural deduction, l-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.

Produktinformation

Utgivningsdatum2002-07-31
Mått155 x 235 x 24 mm
Vikt682 g
FormatInbunden
SpråkEngelska
SerieApplied Logic Series
Antal sidor290
FörlagKluwer Academic Publishers
ISBN9781402007453

Tillhör följande kategorier

I Propositional BI.- 1. Introduction to Part I.- 2. Natural Deduction for Propositional BI.- 3. Algebraic, Topological, Categorical.- 4. Kripke Semantics.- 5. Topological Kripke Semantics.- 6. Propositional BI as a Sequent Calculus.- 7. Towards Classical Propositional BI.- 8. Bunched Logical Relations.- 9. The Sharing Interpretation, I.- II Predicate BI.- 10. Introduction to Part II.- 11. The Syntax of Predicate BI.- 12. Natural Deduction & Sequent Calculus.- 13. Kripke Semantics for Predicate BI.- 14. Topological Kripke Semantics for Predicate BI.- 15. Resource Semantics, Type Theory & Fibred Categories.- 16. The Sharing Interpretation, II.

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)