Abstract
In this paper, the satisfiability problem for a class of proportional sentences is considered. Here a sentence is a set of clauses. A clause is a set of literals. First, it is proposed that a class S 0 of propositional sentences which properly includes the class of propositional Horn sentences. A sentence { C 1 ,…, C n } is in S 0 if there are sets P 1 ,…, P n of positive literals such that (1) P 1 ⊃ P 2 ⊃ … ⊃ P n , (2) P i C i for 1 ⩽ i ⩽ n , and (3) C i − P i is a Horn clause for 1 ⩽ i ⩽ n . Then it is proposed that a new inference rule, based on the resolution principle, by which (un)satisfiability for S 0 in polynomial time can be decided.
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