S5 knowledge without partitions

Synthese 172 (1):145-155 (2010)

Abstract

We study set algebras with an operator 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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