Autoepistemic Belief-revision for Integration of Mutually Inconsistent Knowledge

It is well known that the standard 3-valued logic programs with constraints can be inconsistent. Because of that we can not use it for a data integration where mutually inconsistent information comes from different data sources. We argue that a natural way to answer to this challenge, without collapsing all sentences into inconsistency, is by passing to 4-valued bilattice-based logic (with logic values: true, false, unknown and possible), and by interpreting the inconsistent information with a logic value ”possible”. Differently from the paraconsistent approach we adopt the belief-revision approach, but in such many-valued repairing of inconsistent information we do not eliminate mutually inconsistent information as in the case of a 2-valued database repairing. The original contribution of this paper is an Autoepistemic Many-valued Logic with intuitionistic implication, epistemic negation and Moore’s modal operator: the inference reasoning of this logic is able to change its belief in the truth value of ground facts which come from external sources, and to preserve its internal consistency. We show that each Autoepistemic Logic Program is consistent and we define its minimal many-valued Herbrand models.