Computational Complexity of a Hybridized Horn Fragment of Halpern-Shoham Logic.

We propose hybridization of sub-propositional fragments of Halpern-Shoham logic as a way of obtaining expressive and decidable referential interval temporal logics. In the paper, we hybridize a Horn fragment of Halpern-Shoham logic whose language is restricted in its modal part to necessity modalities, and prove that satisfiability problem in this fragment is $$\\textsc {NP}$$-complete over reflexive or an irreflexive and dense underlying structure of time.