Multi-sorted logic, models and logical geometry

2015/06/18 by Elena Aladova, Aladova, Elena, Aleko Gvaramia +5
Computer Science · #FOS: Computer and information sciences #Logic in Computer Science (cs.LO) #cs.LO

paper · pdf · doi:10.48550/arxiv.1506.06057

18 pages

arxiv created 2015/06/18 · arxiv updated 2015/06/22

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 φ in H. Let X⁰ be an infinite set of variables, Γ be a collection of all finite subsets in X⁰ (collection of sorts), \widetildeΦ be the multi-sorted algebra of formulas. These data define a knowledge base KB(H,Ψ, f). In the paper the notion of isomorphism of knowledge bases is considered. We give sufficient conditions which provide isomorphism of knowledge bases. We also study the problem of necessary and sufficient conditions for isomorphism of two knowledge bases.

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