Minimal Sequent Calculi for Łukasiewicz’s Finitely-Valued Logics

• Autorzy: Pynko, Alexej P

Abstrakty

EN

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].

Słowa kluczowe

EN

sequent calculus; Łukasiewicz’s logics

• Wydawca: Wydawnictwo Uniwersytetu Łódzkiego
• Czasopismo: Bulletin of the Section of Logic
• Rocznik: 2015
• Tom: 44
• Numer: 3-4

Daty

wydano

2015

Twórcy

autor

Pynko, Alexej P

other

Department of Digital Automata Theory (100), V.M. Glushkov Institute of Cybernetics Academician Glushkov, prosp. 40 Kiev, 03680, Ukraine

other

[e-mail]

Identyfikatory

URI

http://hdl.handle.net/11089/17905

DOI

10.18778/0138-0680.44.3.4.04