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Sibirskii Matematicheskii Zhurnal, 2010, Volume 51, Number 4, Pages 838–847 (Mi smj2129)  
This article is cited in 5 scientific papers (total in 5 papers)

On decidability of the decomposability problem for finite theories

A. S. Morozova, D. K. Ponomaryovb

a Sobolev Institute of Mathematics, Novosibirsk, Russia
b Institute of Informatics Systems, Novosibirsk, Russia
Full-text PDF (316 kB) Citations (5)
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Abstract: We consider the decomposability problem for elementary theories, i.e. the problem of deciding whether a theory has a nontrivial representation as a union of two (or several) theories in disjoint signatures. For finite universal Horn theories, we prove that the decomposability problem is $\Sigma _1^0$-complete and, thus, undecidable. We also demonstrate that the decomposability problem is decidable for finite theories in signatures consisting only of monadic predicates and constants.
Keywords: decomposable theory, decomposition of a theory, Horn theory, logic programming, monadic logic.
Received: 09.10.2008
English version:
Siberian Mathematical Journal, 2010, Volume 51, Issue 4, Pages 667–674
DOI: https://doi.org/10.1007/s11202-010-0068-6
Bibliographic databases:
Document Type: Article
UDC: 510.5+510.67
Language: Russian
Citation: A. S. Morozov, D. K. Ponomaryov, “On decidability of the decomposability problem for finite theories”, Sibirsk. Mat. Zh., 51:4 (2010), 838–847; Siberian Math. J., 51:4 (2010), 667–674
Citation in format AMSBIB
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\paper On decidability of the decomposability problem for finite theories
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\pages 838--847
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Сибирский математический журнал Siberian Mathematical Journal
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