Download PDFOpen PDF in browserAn excursion to the border of decidability: between two- and three-variable logic19 pages•Published: June 3, 2023AbstractWith respect to the number of variables the border of decidability lies between 2 and 3: the two-variable fragment of first-order logic, FO2, has an exponential model property and hence NExpTime-complete satisfiability problem, while for the three-variable fragment, FO3, satisfiability is undecidable. In this paper we propose a rich subfragment of FO3, containing full FO2 (without equality), and show that it retains the finite model property and NExpTime complexity. Our fragment is obtained as an extension of the uniform one-dimensional variant of FO3.Keyphrases: finite satisfiability problem, satisfiability problem, three variable logic, two variable logic, uniform one dimensional fragment In: Ruzica Piskac and Andrei Voronkov (editors). Proceedings of 24th International Conference on Logic for Programming, Artificial Intelligence and Reasoning, vol 94, pages 205-223.
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