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: | 27 Jul 2019 12:37 |
| URI: | http://eprints.bbk.ac.uk/id/eprint/13400 |
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