CoNP Complexity for Combinations of Non-normal Modal Logics

We study the complexity of the validity/derivability problem for combinations of non-normal modal logics in the form of logic fusions, possibly extended with simple interaction axioms. We first present cutfree sequent calculi for these logic combinations. Then, we introduce hypersequent calculi with invertible rules, and show that they allow for a coNP proof search procedure. In the last part of the paper, we consider the case of combinations of logics sharing a universal modality. Using the hypersequent calculi, we show that these logics remain coNP-complete, and also provide an equivalent axiomatisation for them.