A DPLL Procedure for the Propositional Product Logic

In the paper, we investigate the deduction problem of a formula from a finite theory in the propositional Product logic from a perspective of automated deduction. Our approach is based on translation of a formula to an equivalent satisfiable finite order clausal theory, consisting of order clauses. An order clause is a finite set of order literals of the form e1 e2 where ei is either a conjunction of propositional atoms or the propositional constant 0 (false) or 1 (true), and is a connective either P or . P and are interpreted by the equality and standard strict linear order on [0;1], respectively. A variant of the DPLL procedure, operating over order clausal theories, is proposed. The DPLL procedure is proved to be refutation sound and complete for finite order clausal theories.

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