We consider a fuzzy linguistic propositional logic having the truth domain as a refined hedge algebra. The syntax and semantic are defined, the resolution is chosen as the inference system. The soundness and completeness of the resolution procedure are proved using semantic tree technique. In order to capture the approximate nature of the resolution inference, we introduce the concept of reliability of resolution inference. The greater the reliability is the more certain the resolution inference is. Finally, we give an optimized resolution procedure which guarantees that each resolution proof has the maximal reliability.

Abstract. The paper introduces a propositional linguistic logic that serves as the basis for automated uncertain reasoning with linguistic information. First, we build a linguistic logic system with truth value domain based on a linear symmetrical hedge algebra. Then, we consider Gödel's t-norm and t-conorm to define the logical connectives for our logic. Next, we present a resolution inference rule, in which two clauses having contradictory linguistic truth values can be resolved. We also give the concept of reliability in order to capture the approximative nature of the resolution inference rule. Finally, we propose a resolution procedure with the maximal reliability.

Abstract. This paper focuses on resolution in linguistic first order logic with truth value taken from linear symmetrical hedge algebra. We build the basic components of linguistic first order logic, including syntax and semantics. We present a resolution principle for our logic to resolve on two clauses having contradictory linguistic truth values. Since linguistic information is uncertain, inference in our linguistic logic is approximate. Therefore, we introduce the concept of reliability in order to capture the natural approximation of the resolution inference rule.

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