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Conference Paper

Labelled Superposition for PLTL


Suda,  Martin
Automation of Logic, MPI for Informatics, Max Planck Society;

Weidenbach,  Christoph
Automation of Logic, MPI for Informatics, Max Planck Society;

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Suda, M., & Weidenbach, C. (2012). Labelled Superposition for PLTL. In N. Bjørner, & A. Voronkov (Eds.), Logic for Programming, Artificial Intelligence, and Reasoning (pp. 391-405). Berlin: Springer.

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This paper introduces a new decision procedure for PLTL based on labelled superposition. Its main idea is to treat temporal formulas as infinite sets of purely propositional clauses over an extended signature. These infinite sets are then represented by finite sets of labelled propositional clauses. The new representation enables the replacement of the complex temporal resolution rule, suggested by existing resolution calculi for PLTL, by a fine grained repetition check of finitely saturated labelled clause sets followed by a simple inference. The completeness argument is based on the standard model building idea from superposition. It inherently justifies ordering restrictions, redundancy elimination and effective partial model building. The latter can be directly used to effectively generate counterexamples of non-valid PLTL conjectures out of saturated labelled clause sets in a straightforward way.