The Semantics and Proof Theory of the Logic of Bunched ImplicationsThis 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. |
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The Semantics and Proof Theory of the Logic of Bunched Implications David J. Pym Limited preview - 2013 |
The Semantics and Proof Theory of the Logic of Bunched Implications David J. Pym No preview available - 2010 |
The Semantics and Proof Theory of the Logic of Bunched Implications David J. Pym No preview available - 2002 |
Common terms and phrases
AA-calculus additive algebraic arrow axiom BI's bunched implications bunches of variables cartesian Chapter classical clauses closed structure combination conjunction connectives consequence consider construction context corresponding defined definition denote dependent type theory Dereliction disjunction example exists extended fibred follows formula function space functor functor categories Galmiche Girard given Grothendieck hE,s implication induction hypothesis introduction rule intuitionistic linear logic intuitionistic logic ISBN Ishtiaq and Pym isomorphism Jr,W judgement Kripke models Kripke resource Kripke semantics Lambek and Scott language Lemma logic programming logical framework maps meta-logic monoidal category monoidal closed multiplicative natural deduction notion O'Hearn and Pym object-logics Plotkin Prawitz predicate premisses preordered commutative monoid prime evaluation proof theory proofs in NBI Prop propositional provable quantifiers redex reduction relation sequent calculus sharing interpretation signature substructural logic symmetric monoidal tensor product theorem tion topological Kripke model topological monoid type theory Vnew worlds
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Page ii - Department of Computer Science, King's College, London, UK SCOPE OF THE SERIES Logic is applied in an increasingly wide variety of disciplines, from the traditional subjects of philosophy and mathematics to the more recent disciplines of cognitive science, computer science, artificial intelligence, and linguistics, leading to new vigor in this ancient subject. Kluwer, through its Applied Logic Series, seeks to provide a home for outstanding books and research monographs in applied logic, and in doing...
Page 272 - Typed Lambda Calculi and Applications, Volume 664 of Lecture Notes in Computer Science, pages 75-90. Springer-Verlag, 1993. (150} [35] EVERT W. BETH. "Semantic Entailmem and Formal Derivability".
Page 273 - Lane, editor, Reports of the Midwest Category Seminar, volume 137 of Lecture Notes in Mathematics, pages 1-38.
Page 279 - ... countable trees. We are deeply indebted to Susanna Ginali. Joe Goguen and Calvin Elgot for their help and encouragement in general and for their contributions to our progress on this problem in particular. This work on compiler correctness was initiated following a series of lectures on algebraic semantics for the Summer School on Foundations of Artificial Intelligence and Computer Science, Pisa, Italy. 19-30 June 1978, by JWT. We were seeking a significant and informative example employing many...
Page 276 - Department of Computer Science, Queen Mary and Westfield College, University of London, London E14NS, UK 2 Department of Computer Science, Royal Holloway, University of London, Egham, Surrey TW20 OEX, UK Abstract.
Page 277 - Mac Lane S. (1971) Categories for the Working Mathematician.
Page i - Pym. The Semantics and Proof Theory of the Logic of Bunched Implications. Applied Logic Series. Kluwer Academic Publishers, 2002.
Bibliographic information
| Title | The Semantics and Proof Theory of the Logic of Bunched Implications Volume 26 of Applied Logic Series |
| Author | David J. Pym |
| Edition | illustrated |
| Publisher | Springer Science & Business Media, 2002 |
| ISBN | 1402007450, 9781402007453 |
| Length | 290 pages |
| Subjects | › › Computers / Programming Languages / General Mathematics / General Mathematics / History & Philosophy Mathematics / Logic Philosophy / Logic |
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