Intuitionistic Truth-Knowledge Symmetric Bilattices for Uncertainty in Intel1igent systems

Differently from pure probability theory the common uncertain information is perception-based and imprecise (L.A. Zadeh, 2002). Human belief, confidence level, etc., are approximate human perceptions and the intelligent systems need a general approximate reasoning logic for them. We propose a family of intuitionistic bilattices with full truth-knowledge duality to be used in logic programming for such uncertain information. The simplest of them, based on intuitionistic truth-functually complete extension of Belnap's 4-valued bilattice, can be used in paraconsistent programming, that is, for knowledge bases with incomplete and inconsistent information. The other two families are useful for an approximate logic theory where the uncertainty in the knowledge about a piece of information is in the form of human granulation cognition types: as an interval-probability belief or as a confidence level. Such logic programs can be parameterized by different kinds of probabilistic conjunctive/disjunctive strategies for their rules, based on intuitionistic implication, which express the user perception-based correlation between observed knowledge facts