Results 21 to 30 of about 275 (133)
Variable-basis Categorically-algebraic Dualities
Fuzzy Information and Engineering, 2014 The manuscript continues our study on developing a categorically-algebraic (catalg) analogue of the theory of natural dualities of D. Clark and B. Davey, which provides a machinery for obtaining topological representations of algebraic structures.
Sergey A. Solovyov
doaj +1 more source
A duality for two-sorted lattices [PDF]
, 2021 A series of representation theorems (some of which discovered very recently) present an alternative view of many classes of algebras related to non-classical logics (e.g.
Rivieccio, Umberto, Jung, Achim
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On duality and model theory for polyadic spaces [PDF]
, 2023 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 completeness,
van Gool, Sam, Marquès, Jérémie
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Remarks on Hyperspaces for Priestley Spaces [PDF]
, 2022 The Vietoris space of a Stone space plays an important role in the coalgebraic approach to modal logic. When generalizing this to positive modal logic, there is a variety of relevant hyperspace constructions based on various topologies on a Priestley ...
Harding, J. +2 more
core
Priestley's Duality from Stone's
Advances in Applied Mathematics, 2000 This is a brief review of various topological dualities for distributive lattices. In essence, Stone duality provides a categorical equivalence between bounded distributive lattices and certain compact \(T_0\) spaces [see \textit{G. Grätzer}, ``Lattice theory''. Freeman and Co., San Francisco (1971; Zbl 0232.06001) for a full characterization].
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Priestley duality for (modal) N4-lattices
EPiC Series in Computing, 2018 N4-lattices are the algebraic semantics of paraconsistent Nelson logic, which was introduced as an inconsistency-tolerant counterpart of the better-known logic of Nelson. Paraconsistent Nelson logic combines interesting features of intuitionistic, classical and many-valued logics (e.g., Belnap-Dunn four-valued logic); recent work has shown that it can ...
Ramon Jansana, Umberto Rivieccio
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Natural dualities in partnership [PDF]
, 2012 Traditionally in natural duality theory the algebras carry no topology and the objects on the dual side are structured Boolean spaces. Given a duality, one may ask when the topology can be swapped to the other side to yield a partner duality (or, better,
Priestley, Hilary +6 more
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Classroom boundaries and teacher agency: Challenges of implementing Ireland's new primary curriculum
The Curriculum Journal, EarlyView.Abstract This article reports on a doctoral study examining teacher agency in one Irish primary school at a timely moment ahead of the implementation of the new Primary Curriculum Framework in September 2025. The framework embeds teacher agency as a central professional principle, yet findings from this study reveal a more cautious and bounded reality.
Máiréad Nally +2 more
wiley +1 more source
Endoprimality without duality [PDF]
, 2004 This paper investigates endoprimal algebras using techniques from universal algebra but not from duality theory, and thereby exposes quite directly how endoprimality ...
Priestley, Hilary +2 more
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Thresholds: The metaphorical foundations of powerful knowledge
The Curriculum Journal, EarlyView.Abstract This paper advances a theoretical account of threshold concepts as metaphorical‐relational structures that reorganise meaning across contexts. Building on conceptual metaphor theory, we propose that threshold concepts can be understood as sites of schema‐level reorganisation: deep, embodied patterns of relational logic that scaffold abstract ...
Maria Karrol +1 more
wiley +1 more source