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    Complexity of equational theory of relational algebras with standard projection elements

    Mikulás, Szabolcs and Sain, I. and Simon, A. (2015) Complexity of equational theory of relational algebras with standard projection elements. Synthese 192 (7), pp. 2159-2182. ISSN 0039-7857.

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    Abstract

    The class \(\mathsf{TPA}\) of t rue p airing a lgebras is defined to be the class of relation algebras expanded with concrete set theoretical projection functions. The main results of the present paper is that neither the equational theory of \(\mathsf{TPA}\) nor the first order theory of \(\mathsf{TPA}\) are decidable. Moreover, we show that the set of all equations valid in \(\mathsf{TPA}\) is exactly on the \(\Pi ^1_1\) level. We consider the class \(\mathsf{TPA}^-\) of the relation algebra reducts of \(\mathsf{TPA}\)’s, as well. We prove that the equational theory of \(\mathsf{TPA}^-\) is much simpler, namely, it is recursively enumerable. We also give motivation for our results and some connections to related work.

    Metadata

    Item Type: Article
    Additional Information: The final publication is available at Springer via http://dx.doi.org/10.1007/s11229-015-0689-1
    Keyword(s) / Subject(s): Logic, Algebraic logic, Finitization problem in algebraic logic, Recursion theory, Theoretical computer science
    School: Birkbeck Schools and Departments > School of Business, Economics & Informatics > Computer Science and Information Systems
    Depositing User: Szabolcs Mikulas
    Date Deposited: 10 Nov 2015 17:50
    Last Modified: 24 May 2016 23:11
    URI: http://eprints.bbk.ac.uk/id/eprint/13400

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