S5 knowledge without partitions

Dov Samet

pp. 145-155

in: Horacio Arló-Costa, Jeffrey Helzner (eds), Foundations of the decision sciences, Synthese 172 (1), 2010.

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.