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Fuzzy linguistic propositional logic based on refined hedge algebra

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.