Geodesic
Strong computability of slices over the logic $\mathrm{GL}$
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 35-47

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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. 
@article{SEMR_2018_15_a2,
     author = {L. L. Maksimova and V. F. Yun},
     title = {Strong computability of slices over the logic $\mathrm{GL}$},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {35--47},
     publisher = {mathdoc},
     volume = {15},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2018_15_a2/}
}
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L. L. Maksimova; V. F. Yun. Strong computability of slices over the logic $\mathrm{GL}$. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 35-47. http://geodesic.mathdoc.fr/item/SEMR_2018_15_a2/