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(2015) Synthese 192 (7).
Complexity of equational theory of relational algebras with standard projection elements
Szabolcs Mikulás, Ildikó Sain, Simon András
pp. 2159-2182
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.
Publication details
DOI: 10.1007/s11229-015-0689-1
Full citation:
Mikulás, S. , Sain, I. , András, S. (2015). Complexity of equational theory of relational algebras with standard projection elements. Synthese 192 (7), pp. 2159-2182.
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