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Logic and Logical Philosophy

Sequent Calculi and Interpolation for Non-Normal Modal and Deontic Logics
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  • Sequent Calculi and Interpolation for Non-Normal Modal and Deontic Logics
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  3. Tom 30 Nr 1 (2021): marzec /
  4. Artykuły

Sequent Calculi and Interpolation for Non-Normal Modal and Deontic Logics

Autor

  • Eugenio Orlandelli Department of Philosophy and Communication Studies, University of Bologna https://orcid.org/0000-0002-4021-8667

DOI:

https://doi.org/10.12775/LLP.2020.018

Słowa kluczowe

non-normal logics, deontic logics, sequent calculi, structural proof theory, interpolation, decidability

Abstrakt

G3-style sequent calculi for the logics in the cube of non-normal modal logics and for their deontic extensions are studied. For each calculus we prove that weakening and contraction are height-preserving admissible, and we give a syntactic proof of the admissibility of cut. This implies that the subformula property holds and that derivability can be decided by a terminating proof search whose complexity is in Pspace. These calculi are shown to be equivalent to the axiomatic ones and, therefore, they are sound and complete with respect to neighbourhood semantics. Finally, a Maehara-style proof of Craig’s interpolation theorem for most of the logics considered is given.

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Logic and Logical Philosophy

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10.10.2020

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ORLANDELLI, Eugenio. Sequent Calculi and Interpolation for Non-Normal Modal and Deontic Logics. Logic and Logical Philosophy [online]. 10 październik 2020, T. 30, nr 1, s. 139–183. [udostępniono 4.7.2025]. DOI 10.12775/LLP.2020.018.
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