Related papers: Piggyback dualities revisited
An algebraic theory of dualities is developed based on the notion of bond algebras. It deals with classical and quantum dualities in a unified fashion explaining the precise connection between quantum dualities and the low temperature…
Bilattices, which provide an algebraic tool for simultaneously modelling knowledge and truth, were introduced by N.D. Belnap in a 1977 paper entitled 'How a computer should think'. Prioritised default bilattices include not only Belnap's…
We develop a duality for (modal) lattices that need not be distributive, and use it to study positive (modal) logic beyond distributivity, which we call weak positive (modal) logic. This duality builds on the Hofmann, Mislove and Stralka…
Gauge duality theory was originated by Freund [Math. Programming, 38(1):47-67, 1987] and was recently further investigated by Friedlander, Mac{\^e}do and Pong [SIAM J. Optm., 24(4):1999-2022, 2014]. When solving some matrix optimization…
It is shown that admissible clauses and quasi-identities of quasivarieties generated by a single finite algebra, or equivalently, the quasiequational and universal theories of their free algebras on countably infinitely many generators, may…
Bilattices (that is, sets with two lattice structures) provide an algebraic tool to model simultaneously the validity of, and knowledge about, sentences in an appropriate language. In particular, certain bilattices have been used to model…
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…
Anyone who has ever worked with a variety~$\boldsymbol{\mathscr{A}}$ of algebras with a reduct in the variety of bounded distributive lattices will know a restricted Priestley duality when they meet one---but until now there has been no…
In this paper, we introduce a novel generalization of the classical property of algebras known as "being alternative," which we term "partially alternative." This new concept broadens the scope of alternative algebras, offering a fresh…
Birkhoff's 1937 dual representation of finite distributive lattices via finite posets was in 1970 extended to a dual representation of arbitrary distributive lattices via compact totally order-disconnected topological spaces by Priestley.…
This paper presents a new method for obtaining small algebras to check the admissibility-equivalently, validity in free algebras-of quasi-identities in a finitely generated quasivariety. Unlike a previous algebraic approach of Metcalfe and…
In general terms duality consists of two descriptions of one physical system by using degrees of freedom of different nature. There are different kinds of dualities and they have been extremely useful to uncover the underlying strong…
We show how classical and quantum dualities, as well as duality relations that appear only in a sector of certain theories ("emergent dualities"), can be unveiled, and systematically established. Our method relies on the use of morphisms of…
It is shown that the relativistic invariance plays a key role in the study of integrable systems. Using the relativistically invariant sine-Gordon equation, the Tzitzeica equation, the Toda fields and the second heavenly equation as dual…
In this article we explain the theory of rigid residue complexes in commutative algebra and algebraic geometry, summarizing the background, recent results and anticipated future results. Unlike all previous approaches to Grothendiec…
The main purpose of this article is to develop an explicit derived deformation theory of algebraic structures at a high level of generality, encompassing in a common framework various kinds of algebras (associative, commutative, Poisson...)…
Profinite algebras are the residually finite compact algebras; their underlying topological spaces are Stone spaces. We extend the theory of profinite algebras to a more general setting of Stone topological algebras. We introduce Stone…
Duality methods are used to generate explicit solutions to nonlinear Hodge systems, demonstrate the well-posedness of boundary value problems, and reveal, via the Hodge-B\"acklund transformation, underlying symmetries among superficially…
We introduce and study a notion of duality for two classes of optimization problems commonly occurring in probability theory. That is, on an abstract measurable space $(\Omega,\mathcal{F})$, we consider pairs $(E,\mathcal{G})$ where $E$ is…
A pair of lower and upper cumulative distribution functions, also called probability box or p-box, is among the most popular models used in imprecise probability theory. They arise naturally in expert elicitation, for instance in cases…