Plausibility and conditional beliefs in paraconsistent modal logic

Abstract

We discuss a paraconsistent modal logic with modalities related to a plausibility preorder on the set of states. One of the modalities expresses support by all states at least as plausible as the present state, the other one is a form of a conditional belief. Our application of the formalism is an epistemic one and it involves the notion of support by the most plausible accessible states. The main technical result obtained so far is a completeness proof for a logic defined by the class of models satisfying a particular closure condition. An alternative, and potentially more general, approach to defining ‘support by the most plausible accessible states’—one based on paraconsistent hybrid logic—is also discussed