Description

• Title:
  Minimal Sequent Calculi for Łukasiewicz’s Finitely-Valued Logics
• Creator:
  Pynko, Alexej P.
• Contributor:
  Department of Digital Automata Theory (100), V.M. Glushkov Institute of Cybernetics Academician Glushkov, prosp. 40 Kiev, 03680, Ukraine.;
  pynko@voliacable.com
• Description:
  The primary objective of this paper, which is an addendum to the author’s [8], is to apply the general study of the latter to Łukasiewicz’s n-valued logics [4]. The paper provides an analytical expression of a 2(n−1)-place sequent calculus (in the sense of [10, 9]) with the cut-elimination property and a strong completeness with respect to the logic involved which is most compact among similar calculi in the sense of a complexity of systems of premises of introduction rules. This together with a quite effective procedure of construction of an equality determinant (in the sense of [5]) for the logics involved to be extracted from the constructive proof of Proposition 6.10 of [6] yields an equally effective procedure of construction of both Gentzen-style [2] (i.e., 2-place) and Tait-style [11] (i.e., 1-place) minimal sequent calculi following the method of translations described in Subsection 4.2 of [7].;
  The work is supported by the National Academy of Sciences of Ukraine.
• Object availability:
  free access
• Rights:
  © Copyright by Alexej P. Pynko, Łódź 2015; © Copyright for this edition by Uniwersytet Łódzki, Łódź 2015
• Date:
  2016.04.28;
  2015
• Type:
  Article
• Language:
  English
• Format:
  application/pdf
• Publisher:
  Wydawnictwo Uniwersytetu Łódzkiego
• Relation:
  Bulletin of the Section of Logic;3/4;
  44
• Subject:
  sequent calculus;
  Łukasiewicz’s logics
• Identifier:
  0138-0680;
  http://hdl.handle.net/11089/17905 ;
  2449-836X;
  10.18778/0138-0680.44.3.4.04
• Data provider:
  Repozytorium Uniwersytetu Łódzkiego
• Can I use it?:
  seek permission
• Type:
  image