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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
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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.
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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