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Humans reason by means of their own language and they can choose and decide alternatives by evaluating semantics of linguistic terms. The fundamental elements in human reasoning are sentences normally containing vague concepts, and these sentences have implicitly or explicitly a truth degree, which is often expressed also by linguistic terms such as more or less false, very false, false, true, very true, more or less true, approximately true, etc. In this article, we introduce a linguistic-valued predicate logic along with an inference system based on resolution. The truth domain of the logic is a refined hedge algebra, generated by a set of truth generators and a set of hedges. The syntax and semantics properties of the logic make sure that every formula has an equisatisfiable formula in conjunctive normal form, and a conjunctive normal form transformation algorithm can be devised. The resolution inference system, parameterized with a threshold of acceptability, is sound and complete. The linguistic-valued predicate logic together with the resolution inference system provides a framework for describing vague statements and mechanizing human reasoning in the presence of vagueness.

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