9 papers
Fischer-Servi logic does not have interpolation
Rodrigo Nicolau Almeida, Nick Bezhanishvili, Simon Lemal
We prove that the Fischer-Servi logic does not have the (Craig) interpolation property. This is obtained by showing that the corresponding class of modal Heyting alge…
Superamalgamation for modal lattices via non-distributive dualities
Rodrigo Nicolau Almeida, Nick Bezhanishvili, Simon Lemal
We show that the variety of modal lattices has the superamalgamation property. As a consequence, we obtain that the weak positive modal logic has the Craig interpolation property.…
Modal Fragments
Nick Bezhanishvili, Balder ten Cate, Arunavo Ganguly +1
We survey systematic approaches to basis-restricted fragments of propositional logic and modal logics, with an emphasis on how expressive power and computational complexity depend…
The Cardinalities of Intervals of Equational Theories and Logics
Juan P. Aguilera, Nick Bezhanishvili, Tenyo Takahashi
We study the cardinality of classes of equational theories (varieties) and logics by applying descriptive set theory. We affirmatively solve open problems raised by Jackson and Lee…
Esakia order-compactifications and locally Esakia spaces
Rodrigo Nicolau Almeida, Guram Bezhanishvili, Nick Bezhanishvili
We introduce Esakia order-compactifications and study how they fit in the general theory of Priestley order-compactifications. We provide an analog of Dwinger's theorem by characte…
Six Proofs of Interpolation for the Modal Logic K
Nick Bezhanishvili, Balder ten Cate, Rosalie Iemhoff
In this chapter, we present six different proofs of Craig interpolation for the modal logic K, each using a different set of techniques (model-theoretic, proof-theoretic, syntactic…
Pre-filtrations, Pre-stable Canonical Rules, and the Kuznetsov-Muravitsky Isomorphism
Nick Bezhanishvili, Antonio Maria Cleani
We introduce pre-filtration and pre-stable canonical rules for the Kuznetsov-Muravitsky system of intuitionistic modal logic and provide a new proof of the Kuznetsov-Muravitsky iso…
Structural Completeness in bi-IPC
Rodrigo Nicolau Almeida, Nick Bezhanishvili
In this note we show that no extension of bi-intuitionistic logic, except for classical logic, is structurally complete; indeed, none of them are passively structurally complete. A…
A Coalgebraic Semantics for Intuitionistic Modal Logic
Rodrigo Nicolau Almeida, Nick Bezhanishvili
We give a new coalgebraic semantics for intuitionistic modal logic with . In particular, we provide a colagebraic representation of intuitionistic descriptive modal frames an…