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S5 knowledge without partitions

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Abstract

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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  1. The Faculty of Management, Tel Aviv University, Tel Aviv, 69978, Israel

    Dov Samet

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  1. Dov Samet
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Correspondence to Dov Samet.

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Samet, D. S5 knowledge without partitions. Synthese 172, 145–155 (2010). https://doi.org/10.1007/s11229-009-9469-0

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  • DOI: https://doi.org/10.1007/s11229-009-9469-0

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