14 papers
The Monadic Grzegorczyk Logic
Guram Bezhanishvili, Mashiath Khan
We develop a semantic criterion for determining whether a given monadic modal logic axiomatizes the one-variable fragment of a predicate modal logic. We show that the criterion app…
Duality Theory for Bounded Lattices: A Comparative Study
Guram Bezhanishvili, Luca Carai, Patrick Morandi
There are numerous generalizations of the celebrated Priestley duality for bounded distributive lattices to the non-distributive setting. The resulting dualities rely on an earlier…
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…
Finite axiomatization of and
Guram Bezhanishvili, Mashiath Khan
We prove that is product matching, and that is axiomatizable by adding to the Gödel…
Failure of Esakia's theorem in the monadic setting
Guram Bezhanishvili, Luca Carai
Esakia's theorem states that Grzegorczyk's logic is the greatest modal companion of intuitionistic propositional calculus. We prove that already the one-variable fragment of intuit…
On the structure of modal and tense operators on a boolean algebra
Guram Bezhanishvili, Andre Kornell
We study the poset NO(B) of necessity operators on a boolean algebra B. We show that NO(B) is a meet-semilattice that need not be distributive. However, when B is complete, NO(B) i…