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Logic and Logical Philosophy

Simple cut elimination proof for hybrid logic
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Simple cut elimination proof for hybrid logic

Authors

  • Andrzej Indrzejczak University of Łódź

DOI:

https://doi.org/10.12775/LLP.2016.004

Keywords

hybrid logic, cut elimination theorem, hypersequent calculi, sequent calculi, geometric conditions

Abstract

In the paper we present a relatively simple proof of cut elimination theorem for variety of hybrid logics in the language with satisfaction operators and universal modality. The proof is based on the strategy introduced originally in the framework of hypersequent calculi but it works well also for standard sequent calculi. Sequent calculus examined in the paper works on so called satisfaction formulae and cover all logics adequate with respect to classes of frames defined by so called geometric conditions.

Author Biography

Andrzej Indrzejczak, University of Łódź

Department of Logic

References

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Indrzejczak, A., “Modal hybrid logic”, Logic and Logical Philosophy, 16, 2–3 (2007): 147–257. DOI:10.12775/LLP.2007.006

Indrzejczak, A., Natural Deduction, Hybrid Systems and Modal Logics, vol. 30 of Trends in Logic, Springer, 2010. DOI:10.1007/978-90-481-8785-0

Indrzejczak, A., and M. Zawidzki, “Decision procedures for some strong hybrid logics”, Logic and Logical Philosophy, 22, 4 (2013): 389–409. DOI:10.12775/LLP.2013.022

Negri, S., “Proof analysis in modal logic”, Journal of Philosophical Logic, 34, 5–6 (2005): 507–544. DOI:10.1007/s10992-005-2267-3

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Seligman, J., “Internalization: The case of hybrid logics”, Journal of Logic and Computation, 11, 5 (2001): 671–689. DOI:10.1093/logcom/11.5.671

Zawidzki, M., Deductive Systems and the Decidability Problem for Hybrid Logics, Univ. of Lódź Press and Jagielonian Univ. Press, 2013.

Logic and Logical Philosophy

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Published

2016-04-04

How to Cite

1.
INDRZEJCZAK, Andrzej. Simple cut elimination proof for hybrid logic. Logic and Logical Philosophy. Online. 4 April 2016. Vol. 25, no. 2, pp. 129-141. [Accessed 14 June 2025]. DOI 10.12775/LLP.2016.004.
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Vol. 25 No. 2 (2016): June

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