Semantic theory of finite lattice-valued propositional logic
Based on the methodology of Pavelka's fuzzy propositional logic, in this paper, by combining L-fuzzy set and classical two-value propositional logic theory, a kind of graded semantic theory in lattice-valued propositional logic based on finite lattice implication algebras is established. The notions of L-tautology and L-contradiction are introduced, and several theorems about the relations among different kinds of L-tautologies are given. From the viewpoint of uncertainty reasoning, the notion of satisfiability with certain level for a set of formulas is also defined. On this basis, the semantic consequence operation concerning a set of formulas is proposed, and the properties of semantic consequence operation and the consistency of fuzzy information are discussed.
semantic theory lattice-valued propositional logic lattice implication algebra l-tautology consistency