Abstract
The aim of this work is to study the notions of elementarily equivalent and isotypic knowledge bases. We prove that isotypic knowledge bases are informationally equivalent.
Similar content being viewed by others
References
Aho A.V., Sagiv Y., Ullman J.D.: Equivalences among relational expressions. SIAM J. Comput. 8(2), 218–246 (1979)
Atzeni P., Aussiello G., Batini C., Moscarini M.: Inclusion and equivalence between relational database schemes. TCS 19, 267–285 (1982)
Baik K.H., Miller L.L.: Topological approach for testing equivalence in heterogenous relational databases. Comput. J. 33(1), 2–10 (1990)
Bancillon F.: On the completeness of query language for relational databases. Lect. Notes CS 64, 112–123 (1978)
Baumslag G., Myasnikov A., Remeslennikov V.N.: Algebraic geometry over groups. I. Algebraic sets and ideal theory. J. Algebra 219, 16–79 (1999)
Beeri, C., Mendelzon, A., Sagiv, Y., Ullman, J.: Equivalence of relational database schemes. SIAM J. on Computing, 10(2), 352–370 (1981)
Beniaminov E.M.: Galois theory of complete relational subalgebras of algebras of relations, logical structures, symmetry. NTI 2, 17–25 (1980)
Beniaminov, E.M.: Algebraic Methods in Database Theory and Representation of Knowledge (Russian). Nauchnyj Mir, Moscow (2003)
Cannon J.J., Holt D.F.: Automorphism group computation and isomorphism testing in finite groups. J. Symb. Comput. 35(3), 241–267 (2003)
Daniyarova Yu.E., Myasnikov A.G., Remeslennikov V.N.: Algebraic geometry over algebraic structures. V. The case of arbitrary signature. Algebra Log. 51(1), 28–40 (2012)
Daniyarova, E.Yu., Myasnikov, A.G., Remeslennikov, V.N.: Algebraic geometry over algebraic structures. II. Foundations. Fundam. Appl. Math. 17(1), 65–106 (2011/2012)
Garsia-Molina H., Ullman J.D., Widom J.: Database Systems. The Complete Book. Pearson Prentice Hall, Englewood Cliffs (2009)
Halmos P.: Algebraic Logic. Chelsea Publishing Company, New York (1962)
Heuer A.: Equivalent schemes in semantic, nested relational, and relational database models. Lect. Notes Comput. Sci. 364, 237–253 (1989)
Hulek K.: Elementary Algebraic Geometry. AMS, Chicago (2000)
Knjazhansky M., Plotkin T.: Knowledge bases over algebraic models: some notes about informational equivalence. Int. J. Knowl. Manag. 8(1), 22–39 (2012)
Krasner M.: Généralisation abstraite de la théorie de Galois. Colloque Int. du CNRS (Algèbre et théorie des nombres) 24, 163–168 (1949)
Los, J.: Quelques remarques, theor‘emes et probl‘emes sur les classes definissables dalg‘ebres. Mathematical Interpretations of Formal Systems, North-Holland, pp. 98–113 (1955)
Marker D.: Model Theory: An Introduction. Springer, Berlin (2002)
Mendelson E.: Introduction to Mathematical Logic. Van Nostrand, New York (1979)
Myasnikov A., Remeslennikov V.: Algebraic geometry over groups II, logical foundations. J. Algebra 234(1), 225–276 (2000)
O’Brien E.A.: Isomorphism testing for p-groups. J. Symb. Comput. 16(3), 305–320 (1993)
Plotkin B.: Universal Algebra, Algebraic Logic and Databases. Kluwer, Dordrecht (1993)
Plotkin, B.: Algebras with the same algebraic geometry. In: Proceedings of the Steklov Institute of Mathematics, MIAN, vol. 242, pp. 176–207 (2003)
Plotkin, B.: Algebraic logic and logical geometry in arbitrary varieties of algebras. In: Proceedings of the conference on group theory, Combinatorics and computing, AMS contemporary math series (2014) (to appear)
Plotkin, B., Aladova, E., Plotkin, E.: Algebraic logic and logically-geometric types in varieties of algebras. J. Algebra Appl. 12(2), Paper No. 1250146 (2013)
Plotkin B., Plotkin T.: Geometrical aspect of databases and knowledge bases. Algebra Universalis 46, 131–161 (2001)
Plotkin, B., Plotkin, T.: Categories of Elementary Sets Over Algebras and Categories of Elementary Algebraic Knowledge. LNCS, vol. 4800, pp. 555–570. Springer, Berlin (2008)
Plotkin, T.: Relational Databases Equivalence Problem. Advances of Databases and Information Systems, pp. 391–404. Springer, Berlin (1996)
Plotkin, T., Knjazhansky, M.: Symmetries of knowledge bases AMAI (Annals of Mathematics and Artificial Intelligence), Special Issue: Applications of Computer Algebra, vol. 64(4). Springer, Berlin, pp. 369–383 (2012)
Rissanen, J.: On the equivalence of database schemes. In: Proceedings of the ACM Symposium Principles of Database Systems, vol. 1, pp. 22–26 (1982)
Roney-Dougal C.M.: Conjugacy of subgroups of the general linear group. Exp. Math. 13(2), 151–163 (2004)
Author information
Authors and Affiliations
Corresponding author
Additional information
We are very grateful to the anonymous reviewers for their valuable and helpful comments and suggestions.
Rights and permissions
About this article
Cite this article
Aladova, E., Plotkin, E. & Plotkin, T. Isotypeness of Models and Knowledge Bases Equivalence. Math.Comput.Sci. 7, 421–438 (2013). https://doi.org/10.1007/s11786-013-0166-5
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11786-013-0166-5