MAKING SOME ISSUES OF IMPLICIT KNOWLEDGE EXPLICIT
Wiebe van der Hoek, John-Jules Meyer · International Journal of Foundations of Computer Science · 1992
We discuss issues of expressibility and completeness of the logic of implicit knowledge (I) and “everybody’s knowledge” (E), as introduced in a system with a number m of epistemic agents by Halpern & Moses. The operator E is defined as a conjunction and corresponds semantically to the union of the m accessibility relations. Dually, the operator I is semantically associated with an intersection, but it is, surprisingly, not equivalent with a disjunction. From the view of Kripke structures there is a related asymmetry: although union can be modally defined, intersection cannot! We discuss consequences (in terms of (in)expressibility, correspondence and completeness) of this property for the epistemic logic under consideration and also present an extension of modal logic in which intersection is expressible.