Knowledge bases and automorphic equivalence of multi-models versus linear spaces and graphs

Marina Knyazhansky; Tatjana Plotkin

Discussiones Mathematicae - General Algebra and Applications (2009)

  • Volume: 29, Issue: 2, page 203-213
  • ISSN: 1509-9415

Abstract

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The paper considers an algebraic notion of automorphic equivalence of models and of multi-models. It is applied to the solution of the problem of informational equivalence of knowledge bases. We show that in the case of linear subjects of knowledge the problem can be reduced to the well-known in computational group theory problems about isomorphism and conjugacy of subgroups of a general linear group.

How to cite

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Marina Knyazhansky, and Tatjana Plotkin. "Knowledge bases and automorphic equivalence of multi-models versus linear spaces and graphs." Discussiones Mathematicae - General Algebra and Applications 29.2 (2009): 203-213. <http://eudml.org/doc/276854>.

@article{MarinaKnyazhansky2009,
abstract = {The paper considers an algebraic notion of automorphic equivalence of models and of multi-models. It is applied to the solution of the problem of informational equivalence of knowledge bases. We show that in the case of linear subjects of knowledge the problem can be reduced to the well-known in computational group theory problems about isomorphism and conjugacy of subgroups of a general linear group.},
author = {Marina Knyazhansky, Tatjana Plotkin},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {knowledge base; information equivalence; automorphic equivalence of models},
language = {eng},
number = {2},
pages = {203-213},
title = {Knowledge bases and automorphic equivalence of multi-models versus linear spaces and graphs},
url = {http://eudml.org/doc/276854},
volume = {29},
year = {2009},
}

TY - JOUR
AU - Marina Knyazhansky
AU - Tatjana Plotkin
TI - Knowledge bases and automorphic equivalence of multi-models versus linear spaces and graphs
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2009
VL - 29
IS - 2
SP - 203
EP - 213
AB - The paper considers an algebraic notion of automorphic equivalence of models and of multi-models. It is applied to the solution of the problem of informational equivalence of knowledge bases. We show that in the case of linear subjects of knowledge the problem can be reduced to the well-known in computational group theory problems about isomorphism and conjugacy of subgroups of a general linear group.
LA - eng
KW - knowledge base; information equivalence; automorphic equivalence of models
UR - http://eudml.org/doc/276854
ER -

References

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  11. [11] B. Plotkin and T. Plotkin, Categories of elementary sets over algebras and categories of elementary algebraic knowledge, LNCS, Springer-Verlag, 4800 (2008), 555-570. Zbl1133.08004
  12. [12] C.M. Roney-Dougal, Conjugacy of subgroups of the general linear group, Experiment. Math. 13 (2) (2004), 151-163. 
  13. [13] C.C. Sims, Computation with Finitely Presented Groups. Cambridge University Press (1994) xiii+604 pp. Zbl0828.20001
  14. [14] A. Tarski, Logic, Semantics, Metamathematics, Oxford University Press, Oxford 1983. Second edition, (First edition 1956). 
  15. [15] M.V. Volkov, The finite basis problem for finite semigroups, Sci. Math. Jpn., 53 (1) (2001), 171-199. Zbl0990.20039

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