  Possibilistic logic is a well-known graded logic of uncertainty suitable to
reason under incomplete information and partially inconsistent knowledge, which
is built upon classical first order logic. There exists for Possibilistic logic
a proof procedure based on a refutation complete resolution-style calculus.
Recently, a syntactical extension of first order Possibilistic logic (called
PLFC) dealing with fuzzy constants and fuzzily restricted quantifiers has been
proposed. Our aim is to present steps towards both the formalization of PLFC
itself and an automated deduction system for it by (i) providing a formal
semantics; (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 a
resolution step. In contrast to standard Possibilistic logic semantics,
truth-evaluation of formulas with fuzzy constants are many-valued instead of
boolean, and consequently an extended notion of possibilistic uncertainty is
also needed.
