Journal of Automated Reasoning

, Volume 46, Issue 1, pp 1–42 | Cite as

Resolution with Order and Selection for Hybrid Logics



We investigate labeled resolution calculi for hybrid logics with inference rules restricted via selection functions and orders. We start by providing a sound and refutationally complete calculus for the hybrid logic \(\mathcal{H}(@,{\downarrow},\mathsf{A})\), even under restrictions by selection functions and orders. Then, by imposing further restrictions in the original calculus, we develop a sound, complete and terminating calculus for the \(\mathcal{H}(@)\) sublanguage. The proof scheme we use to show refutational completeness of these calculi is an adaptation of a standard completeness proof for saturation-based calculi for first-order logic that guarantees completeness even under redundancy elimination. In fact, one of the contributions of this article is to show that the general framework of saturation-based proving for first-order logic with equality can be naturally adapted to saturation-based calculi for other languages, in particular modal and hybrid logics.


Modal logic Resolution calculus Order and selection function constraints Soundness and completeness Termination 


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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Talaris GroupINRIA Nancy Grand EstNancyFrance
  2. 2.Departamento de Computación, FCEyNUniversidad de Buenos AiresBuenos AiresArgentina

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