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pro vyhledávání: '"van Gool, Sam"'
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 correctness in the Coq proof assistant for three modal logics, namely:
Externí odkaz:
http://arxiv.org/abs/2402.10494
Publikováno v:
Electronic Notes in Theoretical Informatics and Computer Science, Volume 3 - Proceedings of MFPS XXXIX (November 23, 2023) entics:12280
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 every type the traditional notion of profinite word coming from automata
Externí odkaz:
http://arxiv.org/abs/2301.12475
Publikováno v:
Logical Methods in Computer Science, Volume 20, Issue 1 (January 26, 2024) lmcs:10937
Join-preserving maps on the discrete time scale $\omega^+$, referred to as time warps, have been proposed as graded modalities that can be used to quantify the growth of information in the course of program execution. The set of time warps forms a si
Externí odkaz:
http://arxiv.org/abs/2302.04668
Autor:
van Gool, Sam, Marquès, Jérémie
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 polyadic Priestley spaces, which we subsequently apply to prove completen
Externí odkaz:
http://arxiv.org/abs/2210.01018
Autor:
Gehrke, Mai, van Gool, Sam
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 mathematics and computer science. Our aim is to get in a fairly full pa
Externí odkaz:
http://arxiv.org/abs/2203.03286
We show that the existence of a first-order formula separating two monadic second order formulas over countable ordinal words is decidable. This extends the work of Henckell and Almeida on finite words, and of Place and Zeitoun on $\omega$-words. For
Externí odkaz:
http://arxiv.org/abs/2201.03089
Graded modalities have been proposed in recent work on programming languages as a general framework for refining type systems with intensional properties. In particular, continuous endomaps of the discrete time scale, or time warps, can be used to qu
Externí odkaz:
http://arxiv.org/abs/2106.06205
Autor:
van Gool, Sam, Marquès, Jérémie
Publikováno v:
In Annals of Pure and Applied Logic February 2024 175(2)
Publikováno v:
Forum Mathematicum, vol. 33, no. 4, 2021, pp. 899-921
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 binary operations are each presented as a pair of partial binary operat
Externí odkaz:
http://arxiv.org/abs/2002.12715
A logic satisfies the interpolation property provided that whenever a formula {\Delta} is a consequence of another formula {\Gamma}, then this is witnessed by a formula {\Theta} which only refers to the language common to {\Gamma} and {\Delta}. That
Externí odkaz:
http://arxiv.org/abs/1803.03003