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Rasiowa–Sikorski Deduction Systems with the Rule of Cut: A Case Study

  • Dorota Leszczyńska-Jasion
  • Mateusz Ignaszak
  • Szymon Chlebowski
Open Access
Article

Abstract

This paper presents Rasiowa–Sikorski deduction systems (R–S systems) for logics \(\mathsf {CPL}\), \(\mathsf {CLuN}\), \(\mathsf {CLuNs}\) and \(\mathsf {mbC}\). For each of the logics two systems are developed: an R–S system that can be supplemented with admissible cut rule, and a \(\mathbf {KE}\)-version of R–S system in which the non-admissible rule of cut is the only branching rule. The systems are presented in a Smullyan-like uniform notation, extended and adjusted to the aims of this paper. Completeness is proved by the use of abstract refutability properties which are dual to consistency properties used by Fitting. Also the notion of admissibility of a rule in an R–S-system is analysed.

Keywords

R–S system The rule of cut Paraconsistent logics \(\mathbf {KE}\) tableau system Inferential erotetic logic 

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© The Author(s) 2018

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Department of Logic and Cognitive Science, Institute of PsychologyAdam Mickiewicz UniversityPoznańPoland

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