Results 1 to 10 of about 917 (136)
Stone-Type Dualities for Separation Logics [PDF]
Logical Methods in Computer Science, 2019 Stone-type duality theorems, which relate algebraic and relational/topological models, are important tools in logic because -- in addition to elegant abstraction -- they strengthen soundness and completeness to a categorical equivalence, yielding a ...
Simon Docherty, David Pym
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Stone Duality for Kolmogorov Locally Small Spaces [PDF]
Symmetry, 2021 In this paper, we prove new versions of Stone Duality. The main version is the following: the category of Kolmogorov locally small spaces and bounded continuous mappings is equivalent to the category of spectral spaces with decent lumps and with bornologies in the lattices of (quasi-) compact open sets as objects and spectral mappings respecting those ...
Artur Piękosz
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Stone Duality for Markov Processes [PDF]
2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science, 2013 We define Aumann algebras, an algebraic analog of probabilistic modal logic. An Aumann algebra consists of a Boolean algebra with operators modeling probabilistic transitions. We prove a Stone-type duality theorem between countable Aumann algebras and countably-generated continuous-space Markov processes.
Dexter Kozen +2 more
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Dioscin initiates dual roles in bladder cancer progression via miR-195–5p/FASN/SLC3A2 axis-mediated cell death mechanisms [PDF]
Translational OncologyEmerging evidence highlights dioscin, a bioactive compound derived from Dioscoreaceae plants, as a promising antitumor agent, yet its regulatory mechanisms in bladder cancer and interaction with microRNAs remain unclear.
Yongchang Lai +6 more
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Unrestricted stone duality for Markov processes [PDF]
2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), 2017 Stone duality relates logic, in the form of Boolean algebra, to spaces. Stone-type dualities abound in computer science and have been of great use in understanding the relationship between computational models and the languages used to reason about them.
Robert Furber +2 more
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Monoidal Extended Stone Duality
Lecture Notes in Computer ScienceAbstractExtensions of Stone-type dualities have a long history in algebraic logic and have also been instrumental for proving results in algebraic language theory. We show how to extend abstract categorical dualities via monoidal adjunctions, subsuming various incarnations of classical extended Stone and Priestley duality as a special case.
Fabian Birkmann +2 more
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Duality for powerset coalgebras [PDF]
Logical Methods in Computer Science, 2022 Let CABA be the category of complete and atomic boolean algebras and complete boolean homomorphisms, and let CSL be the category of complete meet-semilattices and complete meet-homomorphisms. We show that the forgetful functor from CABA to CSL has a left
Guram Bezhanishvili +2 more
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A duality theoretic view on limits of finite structures: Extended version [PDF]
Logical Methods in Computer Science, 2022 A systematic theory of structural limits for finite models has been developed by Nesetril and Ossona de Mendez. It is based on the insight that the collection of finite structures can be embedded, via a map they call the Stone pairing, in a space of ...
Mai Gehrke, Tomáš Jakl, Luca Reggio
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A Coalgebraic Approach to Dualities for Neighborhood Frames [PDF]
Logical Methods in Computer Science, 2022 We develop a uniform coalgebraic approach to J\'onsson-Tarski and Thomason type dualities for various classes of neighborhood frames and neighborhood algebras.
Guram Bezhanishvili +2 more
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Computer Sciences & Mathematics Forum, 2023 Alexander Grothendieck suggested creating a new branch of topology, called “topologie modérée”. In a paper by N. A’Campo, L. Ji, and A. Papadopoulos the authors conclude that no such tame topology has been developed at a purely topological level.
Artur Piękosz
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