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Communication Dans Un Congrès Année : 2007

The complexity of temporal logic with until and since over ordinals

Résumé

We consider the temporal logic with since and until modalities. This temporal logic is expressively equivalent over the class of ordinals to first-order logic thanks to Kamp's theorem. We show that it has a pspace-complete satisfiability problem over the class of ordinals. Among the consequences of our proof, we show that given the code of some countable ordinal α and a formula, we can decide in pspace whether the formula has a model over α. In order to show these results, we introduce a class of simple ordinal automata, as expressive as Büchi ordinal automata. The pspace upper bound for the satisfiability problem of the temporal logic is obtained through a reduction to the nonemptiness problem for the simple ordinal automata. Partially supported by an invited professorship from ENS de Cachan and project AutoMathA (ESF).
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Dates et versions

hal-03203563 , version 1 (20-04-2021)

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Citer

Stéphane Demri, Alexander Rabinovich. The complexity of temporal logic with until and since over ordinals. 14th International Conference Logic for Programming, Artificial Intelligence, and Reasoning ( LPAR 2007 ), Nachum Dershowitz; Andrei Voronkov, Oct 2007, Erevan, Armenia. pp.531-545, ⟨10.1007/978-3-540-75560-9_38⟩. ⟨hal-03203563⟩
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