The complexity of propositional linear temporal logics
Journal of the ACM (JACM)
Automata-Theoretic techniques for modal logics of programs
Journal of Computer and System Sciences
Temporal-logic theorem proving
Temporal-logic theorem proving
Automated deduction in nonclassical logics
Automated deduction in nonclassical logics
A Proof Procedure Using Connection Graphs
Journal of the ACM (JACM)
A Decision Procedure for a Temporal Belief Logic
ICTL '94 Proceedings of the First International Conference on Temporal Logic
A Decision Method for Linear Temporal Logic
Proceedings of the 7th International Conference on Automated Deduction
A resolution method for temporal logic
IJCAI'91 Proceedings of the 12th international joint conference on Artificial intelligence - Volume 1
Non-Clausal Reasoning with Definite Theories
Fundamenta Informaticae
Non-Clausal Reasoning with Definite Theories
Fundamenta Informaticae
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Connection methods have proven their value for efficient automated theorem proving in classical logics. However, these methods have not been extended to temporal logics due to the lack of a subformula property in existing proof procedures. We show that a slightly looser generalized subformula property exists for temporal logics. We then exploit this generalized subformula property to develop a temporal notion of polarities and connections, upon which we base an efficient proof procedure for propositional temporal logic. The proof procedure is structured around semantic tableau augmented with connections, and we propose a number of connection-based strategies. The procedure achieves many of the benefits of connection methods. The method is also sufficiently general to be extensible to other temporal logics. Experimental results indicate substantial speedup resulting from this approach.