On two-variable first-order logic with a partial order
Year: 2025
Type: article
Abstract: The main motivation for this work is the open question of decidability of the satisfiability problem for the two-variable fragment of first-order logic, ${\mathcal{FO}^{2}}$, with one transitive relation. In the presence of equality, the problem can be reduced to the corresponding problem when the transitive relation is required to be a strict partial order. It is known that its finite satisfiability problem is decidable but the decidability of the general satisfiability problem has been resolved only for restricted variants. More precisely, the problem is decidable for the fragment with comparable witnesses in which existential quantifiers are required to be guarded by atoms of the form $x
Source: Journal of Logic and Computation
Authors: Dariusz Marzec, Lidia Tendera
Institution: University of Opole
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $4,533
OpenAlex ID: W7125975836