TY - JOUR
T1 - Multi-Sorted Logic, Models, and Logical Geometry
AU - Aladova, E.
AU - Gvaramia, A.
AU - Plotkin, B.
AU - Plotkin, T.
N1 - Publisher Copyright:
© 2016, Springer Science+Business Media New York.
PY - 2016/5/1
Y1 - 2016/5/1
N2 - 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 Φ˜ 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.
AB - 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 Φ˜ 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.
UR - http://www.scopus.com/inward/record.url?scp=84962295098&partnerID=8YFLogxK
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AN - SCOPUS:84962295098
SN - 1072-3374
VL - 214
SP - 742
EP - 754
JO - Journal of Mathematical Sciences
JF - Journal of Mathematical Sciences
IS - 6
ER -