Infinitary S5-epistemic logic

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It 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.

Original languageEnglish
Pages (from-to)333-342
Number of pages10
JournalMathematical Logic Quarterly
Issue number3
StatePublished - 1997
Externally publishedYes


  • Epistemic logic
  • Infinitary logic
  • Kripke structure
  • Modal logic
  • S5 system


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