Uncertainty reasoning is one of the important issues of many research fields, such as artificial intelligence, knowledge-based systems, data-mining etc.. This paper proposes the theory of uncertainty reasoning in the “If...then...” type uncertainty reasoning mode based on the lattice-valued first-order logic Lvfl. The “If...then...” rule presented here is the rule in which both antecedent and c...

In this paper von Wright’s truth-logic T′′ is considered. It seems that it is a De Morgan four-valued logic DM4 (or Belnap’s four-valued logic) with endomorphism e2. In connection with this many other issues are discussed: twin truth operators, a truth-logic with endomorphism g (or logic Tr), the lattice of extensions of DM4, modal logic V2, Craig interpolation property, von Wright–Segerberg’s ...

For the processing of decision making with uncertainty information, this paper establishes a decision model based on lattice-valued logic and researches the algorithm for extracting the maximum decision rules. Firstly, we further research the lattice-valued fuzzy concept lattice by combining the lattice implication algebra and classical concept lattice; secondly, we define the lattice-valued de...

We introduce a family of modal expansions of Belnap-Dunn four-valued logic and related systems, and interpret them in many-valued Kripke structures. Using algebraic logic techniques and topological duality for modal algebras, and generalizing the so-called twist-structure representation, we axiomatize by means of Hilbert-style calculi the least modal logic over the four-element Belnap lattice a...

Ward and Dilworth 1 introduced the concept of residuated lattices as generalization of ideal lattices of rings. The residuated lattice plays the role of semantics for a multiple-valued logic called residuated logic. Residuated logic is a generalization of intuitionistic logic. Therefore it is weaker than classical logic. Important examples of residuated lattices related to logic are Boolean alg...