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arXiv · 1710.04628

Flat modal fixpoint logics with the converse modality

Sebastian Enqvist
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Abstract

We prove a generic completeness result for a class of modal fixpoint logics corresponding to flat fragments of the two-way mu-calculus, extending earlier work by Santocanale and Venema. We observe that Santocanale and Venema's proof that least fixpoints in the Lindenbaum-Tarski algebra of certain flat fixpoint logics are constructive, using finitary adjoints, no longer works when the converse modality is introduced. Instead, our completeness proof directly constructs a model for a consistent formula, using the induction rule in a way that is similar to the standard completeness proof for propositional dynamic logic. This approach is combined with the concept of a focus, which has previously been used in tableau based reasoning for modal fixpoint logics.

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Sebastian Enqvist. 2017-10-12. Flat modal fixpoint logics with the converse modality. https://arxiv.org/abs/1710.04628

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