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 Sib. Èlektron. Mat. Izv., 2018, Volume 15, Pages 35–47 (Mi semr896)

Mathematical logic, algebra and number theory

Strong computability of slices over the logic $\mathrm{GL}$

L. L. Maksimovaab, V. F. Yunba

a Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia
b Novosibirsk State University, Pirogova Str., 2, 630090, Novosibirsk, Russia

Abstract: In [2] the classification of extensions of the minimal logic $\mathrm{J}$ using slices was introduced and decidability of the classification was proved. We will consider extensions of the logic $\mathrm{GL} = \mathrm{J} + (A \vee \neg A)$. The logic $\mathrm{GL}$ and its extensions have been studied in [8, 9]. In [6], it is established that the logic $\mathrm{GL}$ is strongly recognizable over $\mathrm{J}$, and the family of extensions of the logic $\mathrm{GL}$ is strongly decidable over $\mathrm{J}$. In this paper we prove strong decidability of the classification over $\mathrm{GL}$: for every finite set $Rul$ of axiom schemes and rules of inference, it is possible to efficiently calculate the slice number of the calculus obtained by adding $Rul$ as new axioms and rules to $\mathrm{GL}$.

Keywords: The minimal logic, slices, Kripke frame, decidability, recognizable logic.

 Funding Agency Grant Number Ministry of Education and Science of the Russian Federation ÍØ-6848.2016.1

DOI: https://doi.org/10.17377/semi.2018.15.005

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Document Type: Article
UDC: 510.6
MSC: 03B45
Received December 29, 2016, published January 18, 2018

Citation: L. L. Maksimova, V. F. Yun, “Strong computability of slices over the logic $\mathrm{GL}$”, Sib. Èlektron. Mat. Izv., 15 (2018), 35–47

Citation in format AMSBIB
\Bibitem{MakYun18} \by L.~L.~Maksimova, V.~F.~Yun \paper Strong computability of slices over the logic $\mathrm{GL}$ \jour Sib. \Elektron. Mat. Izv. \yr 2018 \vol 15 \pages 35--47 \mathnet{http://mi.mathnet.ru/semr896} \crossref{https://doi.org/10.17377/semi.2018.15.005} `