Abstract
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.
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Acknowledgements
The author is supported by the Polish National Science Centre grant DEC-2011/02/A/HS1/00395. He thanks Michał Zawidzki for valuable comments and stimulating discussions on hybridization of temporal logics. Moreover, the author thanks Joanna Golińvska-Pilarek, Roman Kontchakov, Carl Schultz, Michael Zakharyaschev and anonymous reviewers for their comments and suggestions on how to improve this paper.
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Wałęga, P.A. (2017). Computational Complexity of a Hybridized Horn Fragment of Halpern-Shoham Logic. In: Ghosh, S., Prasad, S. (eds) Logic and Its Applications. ICLA 2017. Lecture Notes in Computer Science(), vol 10119. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-54069-5_17
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DOI: https://doi.org/10.1007/978-3-662-54069-5_17
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