Multi-Sorted Logic, Models, and Logical Geometry
- Authors: Aladova E.1, Gvaramia A.2, Plotkin B.3, Plotkin T.1
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Affiliations:
- Department of Mathematics, Bar-Ilan University
- Abkhazian State University
- Department of Mathematics, Hebrew University of Jerusalem
- Issue: Vol 214, No 6 (2016)
- Pages: 742-754
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/237504
- DOI: https://doi.org/10.1007/s10958-016-2811-4
- ID: 237504
Cite item
Abstract
Abstract. Let Θ be a variety of algebras, (H,Ψ, f) be a model, where H is an algebra from Θ, Ψ is a set of relation symbols ϕ, f is an interpretation of all the symbols ϕ in H. Let X0 be an infinite set of variables, Γ be the collection of all finite subsets in X0 (the collection of sorts), and \( \tilde{\varPhi} \) be the multi-sorted algebra of formulas. These data define a knowledge base KB(H,Ψ, 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.
About the authors
E. Aladova
Department of Mathematics, Bar-Ilan University
Author for correspondence.
Email: aladovael@mail.ru
Israel, Ramat Gan, 52900
A. Gvaramia
Abkhazian State University
Email: aladovael@mail.ru
Georgia, Sukhumi
B. Plotkin
Department of Mathematics, Hebrew University of Jerusalem
Email: aladovael@mail.ru
Israel, Jerusalem, 91904
T. Plotkin
Department of Mathematics, Bar-Ilan University
Email: aladovael@mail.ru
Israel, Ramat Gan, 52900