An excursion to the border of decidability: between two- and three-variable logic

Oskar Fiuk; Emanuel Kieronski

doi:10.29007/1xns

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An excursion to the border of decidability: between two- and three-variable logic

19 pages•Published: June 3, 2023

Oskar Fiuk and Emanuel Kieronski

Abstract

With 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

Links:	https://easychair.org/publications/paper/KVm2
	https://doi.org/10.29007/1xns

BibTeX entry

@inproceedings{LPAR2023:An_excursion_to_border,
  author    = {Oskar Fiuk and Emanuel Kieronski},
  title     = {An excursion to the border of decidability: between two- and three-variable logic},
  booktitle = {Proceedings of 24th International Conference on Logic for Programming, Artificial Intelligence and Reasoning},
  editor    = {Ruzica Piskac and Andrei Voronkov},
  series    = {EPiC Series in Computing},
  volume    = {94},
  pages     = {205--223},
  year      = {2023},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {https://easychair.org/publications/paper/KVm2},
  doi       = {10.29007/1xns}}

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