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Infinitary S5-Epistemic Logic

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  • HEIFETZ , Aviad

    (School of Mathematical Sciences, Tel Aviv University, Tel Aviv, Israel and CORE, Université catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium)

Abstract

t is known that a theory in S5-epistemic logic with several agents may have numerous models. This is because each such model specifies also what an agent knows about infinite intersections of events, while the expressive power of the logic is limited to finite conjunctions of formulas. We show that this asymmetry between syntax and semantics persists also when infinite conjunctions (up to some given cardinality) are permitted in the language. We develop a strengthened S5-axiomatic system for such infinitary logics, and prove a strong completeness theorem for them. Then we show that in every such logic there is always a theory with more than one model.

Suggested Citation

  • HEIFETZ , Aviad, 1995. "Infinitary S5-Epistemic Logic," LIDAM Discussion Papers CORE 1995057, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:1995057
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    File URL: https://sites.uclouvain.be/core/publications/coredp/coredp1995.html
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