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Logics of Time and Computation cover

Logics of Time and Computation

2nd Edition, Revised and Expanded

Robert Goldblatt

“This is a short but excellent introduction to modal, temporal, and dynamic logic....It manages to cover, in highly readable style, the basic completeness, decidability, and expressability results in a variety of logics of the three kinds considered.”
Rohit Parikh, reviewing the first edition in the Journal of Symbolic Logic

Now revised and significantly expanded, this textbook introduces modal logic and examines the relevance of modal systems for theoretical computer science. Goldblatt sets out a basic theory of normal modal and temporal propositional logics, including issues such as completeness proofs, decidability, first-order definability, and canonicity. The basic theory is then applied to logics of discrete, dense, and continuous time; to the temporal logic of concurrent programs involving the connectives henceforth, next, and until; and to the dynamic logic of regular programs.

New material for the second edition extends the temporal logic of concurrency to branching time, studying a system of Computational Tree Logic that formalizes reasoning about behavior. Dynamic logic is also extended to the case of concurrency, introducing a connective for the parallel execution of commands. A separate section is devoted to the quantificational dynamic logic. Numerous exercises are included for use in the classroom.

Robert Goldblatt is a professor of pure mathematics at the Victoria University of Wellington, New Zealand.


  • Preface to the First Edition
  • Preface to the Second Edition
  • Part One: The Anti-Foundation Axiom
    • 1. Syntax and Semantics
    • 2. Proof Theory
    • 3. Canonical Models and Completeness
    • 4. Filtrations and Decidability
    • 5. Multimodal Languages
    • 6. Temporal Logic
    • 7. Some Topics in Metatheory
  • Part Two: Some Temporal and Computational Logics
    • 8. Logics with Linear Frames
    • 9. Temporal Logic of Concurrency
    • 10. Propositional Dynamic Logic
  • Part Three: First-Order Dynamic Logic
    • 11. Assignments, Substitutions, and Quantifiers
    • 12. Syntax and Semantics
    • 13. Proof Theory
    • 14. Canonical Model and Completeness
  • Bibliography
  • Index


ISBN (Paperback): 9780937073940 (0937073946)
ISBN (Electronic): 9781575868004 (1575868008)
Subject: Linguistics; Logic; Context

Subject: Linguistics; Computational Linguistics

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