The complexity of propositional linear temporal logics
Journal of the ACM (JACM)
A propositional modal logic of time intervals
Journal of the ACM (JACM)
Reasoning about knowledge
Modal logic
The complexity of temporal logic with until and since over ordinals
LPAR'07 Proceedings of the 14th international conference on Logic for programming, artificial intelligence and reasoning
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Sequence logic is a parameterized logic where the formulas are sequences of formulas of some arbitrary underlying logic. The sequence formulas are interpreted in certain linearly ordered sets of models of the underlying logic. This interpretation induces an entailment relation between sequence formulas which strongly depends on which orderings one wishes to consider. Some important classes are: all linear orderings, all dense linear orderings and all (or some specific) wellorderings. For all these classes one can ask for a sound and complete proof system for the entailment relation, as well as for its decidability. For the class of dense linear orderings and all linear orderings we give sound and complete proof systems which also yield decidability (assuming that the underlying logic is sound, complete and decidable). We formulate some open problems on the entailment relation in the case of wellorderings.