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Common knowledge and quantification

Author

Listed:
  • Holger Sturm

    (Institut für Informatik, Universität Leipzig, Augustus-Platz 10-11, 04109 Leipzig, GERMANY)

  • Frank Wolter

    (Institut für Informatik, Universität Leipzig, Augustus-Platz 10-11, 04109 Leipzig, GERMANY)

  • Michael Zakharyaschev

    (Department of Computer Science, King's College, Strand, London WC2R 2LS, U.K.)

Abstract

The paper consists of two parts. The first one is a concise introduction to epistemic (both propositional and predicate) logic with common knowledge operator. As the full predicate logics of common knowledge are not even recursively enumerable, in the second part we introduce and investigate the monodic fragment of these logics which allows applications of the epistemic operators to formulas with at most one free variable. We provide the monodic fragments of the most important common knowledge predicate logics with finite Hilbert-style axiomatizations, prove their completeness, and single out a number of decidable subfragments. On the other hand, we show that the addition of equality to the monodic fragment makes it not recursively enumerable.

Suggested Citation

  • Holger Sturm & Frank Wolter & Michael Zakharyaschev, 2002. "Common knowledge and quantification," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 19(1), pages 157-186.
    • Handle: RePEc:spr:joecth:v:19:y:2002:i:1:p:157-186
    Note: Received: March 7, 2001; revised version: April 4, 2001
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    More about this item

    Keywords

    Epistemic logic; Common knowledge; First-order epistemic logic; Axiomatizability; Monodic fragments.;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • D89 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Other

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