Journal of Automated Reasoning

, Volume 46, Issue 1, pp 1-42

First online:

Resolution with Order and Selection for Hybrid Logics

  • Carlos ArecesAffiliated withTalaris Group, INRIA Nancy Grand Est Email author 
  • , Daniel GorínAffiliated withDepartamento de Computación, FCEyN, Universidad de Buenos Aires

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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