Temporal Logic with Capacity Constraints
FroCoS '07 Proceedings of the 6th international symposium on Frontiers of Combining Systems
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Logical foundations for more expressive declarative temporal logic programming languages
ACM Transactions on Computational Logic (TOCL)
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In this paper, we consider a tractable sub-class of propositional linear time temporal logic, and provide a complete clausal resolution calculus for it. The fragment is important as it can be used to represent simple Büchi automata. We also show that, just as the emptiness check for a Büchi automaton is tractable, the complexity of deciding unsatisfiability, via resolution, of our logic is polynomial (rather than exponential). Consequently, a Büchi automaton can be represented within our logic, and its emptiness can be tractably decided via deductive methods. This may have a significant impact upon approaches to verification, since techniques such as model checking inherently depend on the ability to check emptiness of an appropriate Büchi automaton. Thus, we also discuss how such a logic might form the basis for practical deductive temporal verification.