Journal of Automated Reasoning

, Volume 46, Issue 1, pp 1–42

Resolution with Order and Selection for Hybrid Logics


DOI: 10.1007/s10817-010-9167-0

Cite this article as:
Areces, C. & Gorín, D. J Autom Reasoning (2011) 46: 1. doi:10.1007/s10817-010-9167-0


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 logicResolution calculusOrder and selection function constraintsSoundness and completenessTermination

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