7 papers · 1 filter
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.…
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…
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…