On Multi-Valued and Fuzzy Dia-Logics

The problems of constructing multi-valued and fuzzy dia-logics models are considered. First of all, the origins of dialogue paradigm in ancient science are reviewed. The sources of "Dialogics" as multi-disciplinary area together with various modes of using this term are discussed. Specifically, logical-algebraic models of intelligent agents communication in multi-agent systems based on product lattices (and product logics) are identified by the term "dia-logics". Two basic dia-logics lattices: negotiation (search for consensus) lattice C4 and its dual - disputation lattice D4 are introduced; the appropriate dia-semantics are given. A formal representation of dia-logical bilattice is suggested. Fuzzy dia-logics with truth values in [0,1](2) are constructed; their basic operations are envisaged. The links between bilattice extensions of Dunn-Belnap's semantics and Atanassov's intuitionistic fuzzy sets are mentioned. In the conclusion some basic ideas and principles of fuzzy dia-logics and dia-semantics are stated.