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The propositional product logic is one of the basic fuzzy logics withcontinuous t-norms, exploiting the multiplication t-norm on the unit interval[0,1]. Our aim is to combine well-established automated deduction (theoremproving) with fuzzy inference. As a first step, we devise a modification of theprocedure of Davis, Putnam, Logemann, and Loveland (DPLL) with dichotomousbranching inferring in the product logic. We prove that the procedure isrefutation sound and finitely complete. As a consequence, solutions to thededuction, satisfiability, and validity problems will be proposed for thefinite case. The presented results are applicable to a design of intelligentsystems, exploiting some kind of multi-step fuzzy inference.

A DPLL Procedure with Dichotomous Branching for Propositional Product Logic