The semantics and proof theory of the logic of bunched implications

著者

    • Pym, David J.

書誌事項

The semantics and proof theory of the logic of bunched implications

by David J. Pym

(Applied logic series, v. 26)

Kluwer Academic, c2002

大学図書館所蔵 件 / 13

この図書・雑誌をさがす

注記

Includes bibliographical references (p. 271-282) and index

内容説明・目次

内容説明

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.

目次

  • List of Figures. List of Tables. Preface. Acknowledgments. Foreword. Introduction
  • David J. Pym. Part 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. Part II: Predicate BI. 10. Introduction to Part II. 11. The Syntax of Predicate BI. 12. Natural Deduction & Sequent Calculus For Predicate BI. 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. Bibliography. Index.

「Nielsen BookData」 より

関連文献: 1件中  1-1を表示

詳細情報

  • NII書誌ID(NCID)
    BA58181174
  • ISBN
    • 1402007450
  • 出版国コード
    ne
  • タイトル言語コード
    eng
  • 本文言語コード
    eng
  • 出版地
    Dordrecht
  • ページ数/冊数
    xlix, 287 p.
  • 大きさ
    25 cm
  • 親書誌ID
ページトップへ