Mathematics of modality

書誌事項

Mathematics of modality

Robert Goldblatt

(CSLI lecture notes, no. 43)

CSLI Publications, c1993

  • : pbk

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注記

Includes bibliographical references (p. 259-266) and index

内容説明・目次

内容説明

Modal logic is the study of modalities - expressions that qualify assertions about the truth of statements - like the ordinary language phrases necessarily, possibly, it is known/believed/ought to be, etc., and computationally or mathematically motivated expressions like provably, at the next state, or after the computation terminates. The study of modalities dates from antiquity, but has been most actively pursued in the last three decades, since the introduction of the methods of Kripke semantics, and now impacts on a wide range of disciplines, including the philosophy of language and linguistics ('possible words' semantics for natural language), constructive mathematics (intuitionistic logic), theoretical computer science (dynamic logic, temporal and other logics for concurrency), and category theory (sheaf semantics). This volume collects together a number of the author's papers on modal logic, beginning with his work on the duality between algebraic and set-theoretic modals, and including two new articles, one on infinitary rules of inference, and the other about recent results on the relationship between modal logic and first-order logic. Another paper on the 'Henkin method' in completeness proofs has been substantially extended to give new applications. Additional articles are concerned with quantum logic, provability logic, the temporal logic of relativistic spacetime, modalities in topos theory, and the logic of programs.

目次

  • Introduction
  • 1. Metamathematics of modal logic
  • 2. Semantic analysis of orthologic
  • 3. Orthomodularity is not elementary
  • 4. Arithmetical necessity, provability and intuitionistic logic
  • 5. Diodorean modality in Minkowski spacetime
  • 6. Grothendieck topology as geometric modality
  • 7. The semantics of Hoare's iteration rule
  • 8. An abstract setting for Henkin proofs
  • 9. A framework for infinitary modal logic
  • 10. The McKinsey axiom is not canonical
  • 11. Elementary logics are canonical and pseudo-equational
  • Bibliography
  • Index.

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  • CSLI lecture notes

    Center for the Study of Language and Information, Stanford University (CSLI)

詳細情報

  • NII書誌ID(NCID)
    BA22344062
  • ISBN
    • 1881526240
    • 1881526232
  • LCCN
    93013522
  • 出版国コード
    us
  • タイトル言語コード
    eng
  • 本文言語コード
    eng
  • 出版地
    Stanford, Calif.
  • ページ数/冊数
    v, 273 p.
  • 大きさ
    24 cm
  • 分類
  • 件名
  • 親書誌ID
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