Towards a unified view of logics of incomplete and conflicting information (Linz Seminar on Fuzzy Set Theory 2014)
Résumé
We consider a simplified epistemic logic MEL, whose syntax is a fragment ofthe modal logic KD where an agent can express both beliefs and ignorance state-ments about propositional formulas. It is in fact a standard propositional languageembedded into another one, whose role is to express beliefs about propositions ofthe former. Its semantics can be expressed in terms of subsets of interpretations ofthe inner propositional language, and does not explicitly use accessibility relations.A fragment of MEL is enough to capture three-valued logics of Łukasiewicz andKleene as well as three-valued paraconsistent logics such as the Logic of Paradoxby Priest, and also RM3. We also consider two extensions of MEL.