Algebraic classifications for fragments of first-order logic and beyond
Abstract
Complexity and decidability of logics is a major research area involving a huge range of different logical systems. This calls for a unified and systematic approach for the field. We introduce a research program based on an algebraic approach to complexity classifications of fragments of first-order logic (FO) and beyond. Our base system GRA, or general relation algebra, is equiexpressive with FO. It resembles cylindric algebra but employs a finite signature with only seven different operators. We provide a comprehensive classification of the decidability and complexity of the systems obtained by limiting the allowed sets of operators. We also give algebraic characterizations of the best known decidable fragments of FO. Furthermore, to move beyond FO, we introduce the notion of a generalized operator and briefly study related systems.
Keywords
Cite
@article{arxiv.2005.01184,
title = {Algebraic classifications for fragments of first-order logic and beyond},
author = {Reijo Jaakkola and Antti Kuusisto},
journal= {arXiv preprint arXiv:2005.01184},
year = {2023}
}
Comments
36 pages, extended version of the CSL 2023 paper "Complexity classifications via algebraic logic," updates the earlier versions