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Resolution with Order and Selection for Hybrid Logics

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Abstract

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.

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Authors and Affiliations

  1. Talaris Group, INRIA Nancy Grand Est, Nancy, France

    Carlos Areces

  2. Departamento de Computación, FCEyN, Universidad de Buenos Aires, Buenos Aires, Argentina

    Daniel Gorín

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  1. Carlos Areces
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Correspondence to Carlos Areces.

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Areces, C., Gorín, D. Resolution with Order and Selection for Hybrid Logics. J Autom Reasoning 46, 1–42 (2011). https://doi.org/10.1007/s10817-010-9167-0

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