Tipus de document

Article

Versió

Versió publicada

Data de publicació

Llicència de publicació

cc-by (c) Martins, Miguel et al., 2025
Si us plau utilitzeu sempre aquest identificador per citar o enllaçar aquest document: https://hdl.handle.net/2445/231338

Local tabularity is decidable for bi-intermediate logics of trees and of co-trees

Títol de la revista

Director/Tutor

ISSN de la revista

Títol del volum

Resum

A bi-Heyting algebra validates the Gödel-Dummett axiom (p → q) ∨ (q → p) iff the poset of its prime filters is a disjoint union of co-trees (i.e., order duals of trees). Bi-Heyting algebras of this kind are called bi-Gödel algebras and form a variety that algebraizes the extension bi-GD of bi-intuitionistic logic axiomatized by the Gödel-Dummett axiom. In this paper we establish the decidability of the problem of determining if a finitely axiomatizable extension of bi-GD is locally tabular. Notably, if L is an axiomatic extension of bi-GD, then L is locally tabular iff L is not contained in Log(F C), the logic of a particular family of finite co-trees, called the finite combs. We prove that Log(F C) is finitely axiomatizable. Since this logic also has the finite model property, it is therefore decidable. Thus, the above characterization of local tabularity ensures the decidability of the aforementioned problem.

Citació

Citació

MARTINS, Miguel and MORASCHINI, Tommaso. Local tabularity is decidable for bi-intermediate logics of trees and of co-trees. Annals of Pure and Applied Logic. 2025. Vol. 176, num. 5. ISSN 0168-0072. [consulted: 11 of September of 2026]. Available at: https://hdl.handle.net/2445/231338

Exportar metadades

JSON - METS

Compartir registre