A family of graded epistemic logics

Abstract

Multi-Agent Epistemic Logic has been investigated in Computer Science [5] to represent and reason about agents or groups of agents knowledge and beliefs. Some extensions aimed to reasoning about knowledge and probabilities [4] and also with a fuzzy semantics have been proposed [6,13]. This paper introduces a parametric method to build graded epistemic logics inspired in the systematic method to build Multi-valued Dynamic Logics introduced in [11,12]. The parameter in both methods is the same: an action lattice [9]. This algebraic structure supports a generic space of agent knowledge operators, as choice, composition and closure (as a Kleene algebra), but also a proper truth space for possible non bivalent interpretation of the assertions (as a residuated lattice).