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Fundamentalnaya i Prikladnaya Matematika, 2014, Volume 19, Issue 3, Pages 5–22
(Mi fpm1589)
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This article is cited in 1 scientific paper (total in 1 paper)
Multi-sorted logic, models, and logical geometry
E. Aladovaab, A. Gvaramiac, B. Plotkind, T. Plotkinb a Penza State University, Penza, Russia
b Bar-Ilan University, Ramat Gan, Israel
c Abkhazian State University, Sukhumi, Abkhazia
d Hebrew University of Jerusalem, Israel
Abstract:
Let $\Theta$ be a variety of algebras, $(H,\Psi,f)$ be a model, where $H$ is an algebra from $\Theta$, $\Psi$ is a set of relation symbols $\varphi$, $f$ is an interpretation of all the symbols $\varphi$ in $H$. Let $X^0$ be an infinite set of variables, $\Gamma$ be the collection of all finite subsets in $X^0$ (the collection of sorts), and $\tilde\Phi$ be the multi-sorted algebra of formulas. These data define a knowledge base $\mathrm{KB}(H,\Psi,f)$. In this paper, the notion of isomorphism of knowledge bases is considered. We give sufficient conditions that provide isomorphism of knowledge bases. We also study the problem of necessary and sufficient conditions for isomorphism of two knowledge bases.
Citation:
E. Aladova, A. Gvaramia, B. Plotkin, T. Plotkin, “Multi-sorted logic, models, and logical geometry”, Fundam. Prikl. Mat., 19:3 (2014), 5–22; J. Math. Sci., 214:6 (2016), 742–754
Linking options:
https://www.mathnet.ru/eng/fpm1589 https://www.mathnet.ru/eng/fpm/v19/i3/p5
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Abstract page: | 401 | Full-text PDF : | 224 | References: | 49 |
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