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Infinitary S5‐Epistemic Logic
Author(s) -
Heifetz Aviad
Publication year - 1997
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.19970430306
Subject(s) - mathematics , axiom , expressive power , gödel's completeness theorem , cardinality (data modeling) , completeness (order theory) , model theory , discrete mathematics , syntax , calculus (dental) , algebra over a field , pure mathematics , computer science , theoretical computer science , artificial intelligence , medicine , mathematical analysis , geometry , dentistry , data mining
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.