55 citations · 134 across the 26 of their papers we have counts for
21 papers · 1 filter
Teams, Truthmakers, Translations
Maria Aloni, Alexandru Baltag, Johan van Benthem +2
We present a faithful translation from Aloni's logic BSL into a classical modal logic over semilattices combining ideas from earlier modal translations of truthmaker semantics with…
Modal Measurable Logics via a Modal Loomis-Sikorski Representation Theorem
Nick Bezhanishvili, Jim de Groot, Lawrence S. Moss
We investigate a modal extension of the infinitary classical logic with countable meets and joins, formulated with an eye toward measure-theoretic work in dynamical systems and in…
A calculus for modal compact Hausdorff spaces
Nick Bezhanishvili, Luca Carai, Silvio Ghilardi +1
The symmetric strict implication calculus is a modal calculus for compact Hausdorff spaces. This is established through de Vries duality, linking compact Hausdorff…
On Shehtman's Two Problems
Guram Bezhanishvili, Nick Bezhanishvili, Joel Lucero-Bryan +1
We provide partial solutions to two problems posed by Shehtman concerning the modal logic of the Čech-Stone compactification of an ordinal space. We use the Continuum Hypothesis to…
The Intermediate Logic of Convex Polyhedra
Sam Adam-Day, Nick Bezhanishvili, David Gabelaia +1
We investigate a recent semantics for intermediate (and modal) logics in terms of polyhedra. The main result is a finite axiomatisation of the intermediate logic of the class of al…
Degrees of the finite model property: the antidichotomy theorem
Guram Bezhanishvili, Nick Bezhanishvili, Tommaso Moraschini
A classic result in modal logic, known as the Blok Dichotomy Theorem, states that the degree of incompleteness of a normal extension of the basic modal logic is or $2^{…
Bi-intermediate logics of trees and co-trees
N. Bezhanishvili, M. Martins, T. Moraschini
A bi-Heyting algebra validates the Gödel-Dummett axiom iff the poset of its prime filters is a disjoint union of co-trees (i.e., order duals of trees). Bi-H…
Intermediate logics in the setting of team semantics
Nick Bezhanishvili, Fan Yang
Several authors have recently defined intuitionistic logic based on team semantics (tIPC). In this paper we provide two alternative approaches to intermediate logics in the team se…
Blok-Esakia Theorems via Stable Canonical Rules
Nick Bezhanishvili, Antonio Maria Cleani
We present a new uniform method for studying modal companions of superintuitionistic rule systems and related notions, based on the machinery of stable canonical rules. Using this…
Positive Modal Logic Beyond Distributivity
Nick Bezhanishvili, Anna Dmitrieva, Jim de Groot +1
We develop a duality for (modal) lattices that need not be distributive, and use it to study positive (modal) logic beyond distributivity, which we call weak positive (modal) logic…
Admissibility of -Inference Rules: interpolation, model completion, and contact algebras
Nick Bezhanishvili, Luca Carai, Silvio Ghilardi +1
We devise three strategies for recognizing admissibility of non-standard inference rules via interpolation, uniform interpolation, and model completions. We apply our machinery to…
Choice-free Stone duality
Nick Bezhanishvili, Wesley H. Holliday
The standard topological representation of a Boolean algebra via the clopen sets of a Stone space requires a nonconstructive choice principle, equivalent to the Boolean Prime Ideal…
Polyhedral completeness of intermediate logics: the Nerve Criterion
Sam Adam-Day, Nick Bezhanishvili, David Gabelaia +1
We investigate a recently-devised polyhedral semantics for intermediate logics, in which formulas are interpreted in n-dimensional polyhedra. An intermediate logic is polyhedrally…
Profiniteness and representability of spectra of Heyting algebras
G. Bezhanishvili, N. Bezhanishvili, T. Moraschini +1
We prove that there exist profinite Heyting algebras that are not isomorphic to the profinite completion of any Heyting algebra. This resolves an open problem from 2009. More gener…
A Study of Subminimal Logics of Negation and their Modal Companions
Nick Bezhanishvili, Almudena Colacito, Dick de Jongh
We study propositional logical systems arising from the language of Johansson's minimal logic and obtained by weakening the requirements for the negation operator. We present their…
Diego's Theorem for nuclear implicative semilattices
Guram Bezhanishvili, Nick Bezhanishvili, Luca Carai +3
We prove that the variety of nuclear implicative semilattices is locally finite, thus generalizing Diego's Theorem. The key ingredients of our proof include the coloring technique…
Coalgebraic Geometric Logic: Basic Theory
Nick Bezhanishvili, Jim de Groot, Yde Venema
Using the theory of coalgebra, we introduce a uniform framework for adding modalities to the language of propositional geometric logic. Models for this logic are based on coalgebra…
Tarski's Theorem on Intuitionistic logic, for polyhedra
Nick Bezhanishvili, Vincenzo Marra, Daniel McNeill +1
In 1938, Tarski proved that a formula is not intuitionistically valid if, and only if, it has a counter-model in the Heyting algebra of open sets of some topological space. In fact…
Canonical formulas for k-potent commutative, integral, residuated lattices
Nick Bezhanishvili, Nick Galatos, Luca Spada
Canonical formulas are a powerful tool for studying intuitionistic and modal logics. Actually, they provide a uniform and semantic way to axiomatise all extensions of intuitionisti…
Changing a semantics: opportunism or courage?
H. Andréka, J. F. A. K. van Benthem, N. Bezhanishvili +1
The generalized models for higher-order logics introduced by Leon Henkin, and their multiple offspring over the years, have become a standard tool in many areas of logic. Even so,…
Duality and universal models for the meet-implication fragment of IPC
Nick Bezhanishvili, Dion Coumans, Samuel J. van Gool +1
In this paper we investigate the fragment of intuitionistic logic which only uses conjunction (meet) and implication, using finite duality for distributive lattices and universal m…