ABSTRACT
In this paper we describe a three-valued logic of belief, a member of the family of many-valued modal logics introduced by M. Fitting. This logic possesses the axioms of positive and negative introspection along with an interesting version of axiom Τ which asserts that a known fact cannot be false, even if it has not been verified yet. The proposed logic is of computational interest for two reasons (i) it can also be seen as the logic describing the epistemic consensus of two interrelated agents: a K45 agent dominating an S5 agent, and (ii) its satisfiability problem is NP-complete. The latter should be contrasted to the well-known fact that the satisfiability problem for the above mentioned epistemic logics with two or more agents is PSPACE-complete.
