27 citations · 64 across the 13 of their papers we have counts for
14 papers
Uniform Interpolation
Sam van Gool
Uniform interpolation is a strengthening of interpolation that holds for certain propositional logics. The starting point of this chapter is a theorem of A. Pitts, which shows that…
Mechanised uniform interpolation for modal logics K, GL, and iSL
Hugo Férée, Iris van der Giessen, Sam van Gool +1
The uniform interpolation property in a given logic can be understood as the definability of propositional quantifiers. We mechanise the computation of these quantifiers and prove…
Deciding Equations in the Time Warp Algebra
Sam van Gool, Adrien Guatto, George Metcalfe +1
Join-preserving maps on the discrete time scale , referred to as time warps, have been proposed as graded modalities that can be used to quantify the growth of information in…
Profinite lambda-terms and parametricity
Sam van Gool, Paul-André Melliès, Vincent Moreau
Combining ideas coming from Stone duality and Reynolds parametricity, we formulate in a clean and principled way a notion of profinite lambda-term which, we show, generalizes at ev…
On duality and model theory for polyadic spaces
Sam van Gool, Jérémie Marquès
This paper is a study of first-order coherent logic from the point of view of duality and categorical logic. We prove a duality theorem between coherent hyperdoctrines and open pol…
Topological Duality for Distributive Lattices: Theory and Applications
Mai Gehrke, Sam van Gool
This book is a course in Stone-Priestley duality theory, with applications to logic and theoretical computer science. Our target audience are graduate students and researchers in m…
Priestley duality for MV-algebras and beyond
Wesley Fussner, Mai Gehrke, Sam van Gool +1
We provide a new perspective on extended Priestley duality for a large class of distributive lattices equipped with binary double quasioperators. Under this approach, non-lattice b…
An open mapping theorem for finitely copresented Esakia spaces
Samuel J. van Gool, Luca Reggio
We prove an open mapping theorem for the topological spaces dual to finitely presented Heyting algebras. This yields in particular a short, self-contained semantic proof of the uni…
Pro-aperiodic monoids via saturated models
Samuel J. v. Gool, Benjamin Steinberg
We apply Stone duality and model theory to study the structure theory of free pro-aperiodic monoids. Stone duality implies that elements of the free pro-aperiodic monoid may be vie…
A model-theoretic characterization of monadic second order logic on infinite words
Silvio Ghilardi, Samuel J. van Gool
Monadic second order logic and linear temporal logic are two logical formalisms that can be used to describe classes of infinite words, i.e., first-order models based on the natura…
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…
Distributive envelopes and topological duality for lattices via canonical extensions
Mai Gehrke, Sam Van Gool
We establish a topological duality for bounded lattices. The two main features of our duality are that it generalizes Stone duality for bounded distributive lattices, and that the…
Sheaf representations of MV-algebras and lattice-ordered abelian groups via duality
Mai Gehrke, Samuel J. van Gool, Vincenzo Marra
We study representations of MV-algebras -- equivalently, unital lattice-ordered abelian groups -- through the lens of Stone-Priestley duality, using canonical extensions as an esse…
Duality and canonical extensions for stably compact spaces
Sam van Gool
We construct a canonical extension for strong proximity lattices in order to give an algebraic, point-free description of a finitary duality for stably compact spaces. In this sett…