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Complexity Classifications via Algebraic Logic

Authors Reijo Jaakkola , Antti Kuusisto

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Author Details

Reijo Jaakkola
  • Tampere University, Finland
Antti Kuusisto
  • Tampere University, Finland
  • University of Helsinki, Finland

Funding

The authors were funded by the Academy of Finland project Theory of computational logics, grant numbers 324435, 328987 (to December 2021) and 352419, 352420, 353027 (2022 onwards).
  • Jaakkola, Reijo: Academy of Finland project Theory of Computational Logics, grant 328987
  • Kuusisto, Antti: Academy of Finland project Theory of Computational Logics, grants 324435, 328987, 352419, 352420, 353027

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Reijo Jaakkola and Antti Kuusisto. Complexity Classifications via Algebraic Logic. In 31st EACSL Annual Conference on Computer Science Logic (CSL 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 252, pp. 27:1-27:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.CSL.2023.27

Abstract

Complexity and decidability of logics is an active research area involving a wide range of different logical systems. We introduce an algebraic approach to complexity classifications of computational logics. Our base system GRA, or general relation algebra, is equiexpressive with first-order logic FO. It resembles cylindric algebra but employs a finite signature with only seven different operators, thus also giving a very succinct characterization of the expressive capacities of first-order logic. We provide a comprehensive classification of the decidability and complexity of the systems obtained by limiting the allowed sets of operators of GRA. We also discuss variants and extensions of GRA, and we provide algebraic characterizations of a range of well-known decidable logics.

Subject Classification

ACM Subject Classification
  • Theory of computation → Logic
Keywords
  • Decidability
  • complexity
  • algebraic logic
  • fragments of first-order logic

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