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  1.  94
    Defining Knowledge in Terms of Belief: The Modal Logic Perspective.Joseph Y. Halpern, Dov Samet & Ella Segev - 2009 - Review of Symbolic Logic 2 (3):469-487.
    The question of whether knowledge is definable in terms of belief, which has played an important role in epistemology for the last 50 years, is studied here in the framework of epistemic and doxastic logics. Three notions of definability are considered: explicit definability, implicit definability, and reducibility, where explicit definability is equivalent to the combination of implicit definability and reducibility. It is shown that if knowledge satisfies any set of axioms contained in S5, then it cannot be explicitly defined in (...)
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  2.  33
    On Definability in Multimodal Logic.Joseph Y. Halpern, Dov Samet & Ella Segev - 2009 - Review of Symbolic Logic 2 (3):451-468.
    Three notions of definability in multimodal logic are considered. Two are analogous to the notions of explicit definability and implicit definability introduced by Beth in the context of first-order logic. However, while by Beth’s theorem the two types of definability are equivalent for first-order logic, such an equivalence does not hold for multimodal logics. A third notion of definability, reducibility, is introduced; it is shown that in multimodal logics, explicit definability is equivalent to the combination of implicit definability and reducibility. (...)
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  3.  43
    S5 Knowledge Without Partitions.Dov Samet - 2010 - Synthese 172 (1):145 - 155.
    We study set algebras with an operator (SAO) that satisfy the axioms of S5 knowledge. A necessary and sufficient condition is given for such SAOs that the knowledge operator is defined by a partition of the state space. SAOs are constructed for which the condition fails to hold. We conclude that no logic singles out the partitional SAOs among all SAOs.
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    S5 Knowledge Without Partitions.Dov Samet - 2010 - Synthese 172 (1):145-155.
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  5.  20
    Counterfactuals in Wonderland.Dov Samet - manuscript
    The literary source of the main ideas in Aumann's article "Backward Induction and Common Knowledge of Rationality" is exposed and analyzed. The primordial archetypal images that underlie both this literary source and Aumann's work are delineated and are used to explain the great emotive impact that this work had on the community of game theorists.
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