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Possibilistic logic is a well-known graded logic of uncertainty suitable toreason under incomplete information and partially inconsistent knowledge, whichis built upon classical first order logic. There exists for Possibilistic logica proof procedure based on a refutation complete resolution-style calculus.Recently, a syntactical extension of first order Possibilistic logic (calledPLFC) dealing with fuzzy constants and fuzzily restricted quantifiers has beenproposed. Our aim is to present steps towards both the formalization of PLFCitself and an automated deduction system for it by (i) providing a formalsemantics; (ii) defining a sound resolution-style calculus by refutation; and(iii) describing a first-order proof procedure for PLFC clauses based on (ii)and on a novel notion of most general substitution of two literals in aresolution step. In contrast to standard Possibilistic logic semantics,truth-evaluation of formulas with fuzzy constants are many-valued instead ofboolean, and consequently an extended notion of possibilistic uncertainty isalso needed.

On the Semantics and Automated Deduction for PLFC, a Logic of Possibilistic Uncertainty and Fuzziness