The Computational Complexity of Satisfiability of Temporal Horn Formulas in Propositional Linear-Time Temporal Logic

Since the invention of Prolog, a programming language based on classical first-order logic, many people have tried to extend it using similiar ideas and redefine the semantics of the extended Prolog in terms of nonclassical logics [3,5,81. The success of a programming language based on nonclassical logics usually lies in the new definiton of Horn formulas and SLD-resolution-like inference rule. For modal logic and temporal logic, the corresponding definitions of Horn formulas have been available [1,4,5]. It is thus theoretically interesting to know the inherent complexity of the satisfiability problem for propositional temporal Horn formulas. In this paper we shah investigate the complexity of the satisfiability problem for two Horn fragments in propositional linear-time temporal logic, The first one contains two temporal connectives 0 (eventuality> and D (always) only and the second one contains an additional next-time connective o. It has been shown that the satisfiability problem for Iinear-time temporai logic whose tempo-