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The structure of slices over minimal logic

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Abstract

In [1], we introduced a classification of extensions of Johansson’s minimal logic J by means of slices and proved the decidability of the classification. In this article, we find sufficiently simple necessary conditions for the maximality of logics in the slices formulated in terms of frames. This makes it possible to describe an efficient procedure for computing the slice number of any finitely axiomatizable logic over J. The maximal logics of the upper slices are written down explicitly.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics Novosibirsk State University, Novosibirsk, Russia

    L. L. Maksimova

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  1. L. L. Maksimova
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Correspondence to L. L. Maksimova.

Additional information

The author was partially supported by the State Maintenance Problem for the Leading Scientific Schools (Grant NSh–860.2014.1).

Novosibirsk. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 57, No. 5, pp. 1078–1087, September–October, 2016; DOI: 10.17377/smzh.2016.57.513.

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Maksimova, L.L. The structure of slices over minimal logic. Sib Math J 57, 841–848 (2016). https://doi.org/10.1134/S003744661605013X

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  • DOI: https://doi.org/10.1134/S003744661605013X

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