55 citations · 134 across the 26 of their papers we have counts for
29 papers
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…
Weak Simplicial Bisimilarity for Polyhedral Models and SLCS_eta -- Extended Version
Nick Bezhanishvili, Vincenzo Ciancia, David Gabelaia +4
In the context of spatial logics and spatial model checking for polyhedral models -- mathematical basis for visualisations in continuous space -- we propose a weakening of simplici…
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…
A Coalgebraic Approach to Dualities for Neighborhood Frames
Guram Bezhanishvili, Nick Bezhanishvili, Jim de Groot
We develop a uniform coalgebraic approach to Jónsson-Tarski and Thomason type dualities for various classes of neighborhood frames and neighborhood algebras. In the first part of t…
The Topological Mu-Calculus: completeness and decidability
Alexandru Baltag, Nick Bezhanishvili, David Fernández-Duque
We study the topological -calculus, based on both Cantor derivative and closure modalities, proving completeness, decidability and FMP over general topological spaces, as well a…
Geometric Model Checking of Continuous Space
Nick Bezhanishvili, Vincenzo Ciancia, David Gabelaia +3
Topological Spatial Model Checking is a recent paradigm where model checking techniques are developed for the topological interpretation of Modal Logic. The Spatial Logic of Closur…
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…
Minimisation in Logical Form
Nick Bezhanishvili, Marcello Bonsangue, Helle Hvid Hansen +4
Stone-type dualities provide a powerful mathematical framework for studying properties of logical systems. They have recently been fruitfully explored in understanding minimisation…
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…
A New Game Equivalence and its Modal Logic
Johan van Benthem, Nick Bezhanishvili, Sebastian Enqvist
We revisit the crucial issue of natural game equivalences, and semantics of game logics based on these. We present reasons for investigating finer concepts of game equivalence than…
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…