Related papers: Distributive bilattices from the perspective of na…
This paper focuses on natural dualities for varieties of bilattice-based algebras.Such varieties have been widely studied as semantic models in situations where information is incomplete or inconsistent. The most popular tool for studying…
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…
There are numerous generalizations of the celebrated Priestley duality for bounded distributive lattices to the non-distributive setting. The resulting dualities rely on an earlier foundational work of such authors as Nachbin,…
We first present a Priestley-style dualitiy for the classes of algebras that are the algebraic counterpart of some congruential, finitary and filter-distributive logic with theorems. Then we analyze which properties of the dual spaces…
We provide a simple natural duality for the varieties generated by the negation- and implication- free reduct of a finite MV-chain. We study these varieties through the dual equivalence thus obtained. For example, we fully characterize…
We introduce a general framework for generating dualities between categories of partial orders and categories of ordered Stone spaces; we recover in particular the classical Priestley duality for distributive lattices and establish several…
We develop dualities for complete perfect distributive quasi relation algebras and complete perfect distributive involutive FL-algebras. The duals are partially ordered frames with additional structure. These frames are analogous to the…
We present a technique for deriving certain new natural dualities for any variety of algebras generated by a finite Heyting chain. The dualities we construct are tailored to admit a transparent translation to the more pictorial…
This paper studies algebras arising as algebraic semantics for logics used to model reasoning with incomplete or inconsistent information. In particular we study, in a uniform way, varieties of bilattices equipped with additional…
This paper fills a gap in the literature on natural duality theory. It concerns dual representations of categories of distributive-lattice-based algebras in which the lattice reducts are not assumed to have bounds. The development of theory…
In natural duality theory, the piggybacking technique is a valuable tool for constructing dualities. As originally devised by Davey and Werner, and extended by Davey and Priestley, it can be applied to finitely generated quasivarieties of…
This is a survey on selected developments in the theory of natural dualities where the author had the opportunity to make with his foreign colleagues several breakthroughs and move the theory forward. It is aimed as author's reflection on…
Information algebras arise from the idea that information comes in pieces which can be aggregated or combined into new pieces, that information refers to questions and that from any piece of information, the part relevant to a given…
The double point relation defines a natural theory of algebraic cobordism for bundles on varieties. We construct a simple basis (over the rationals) of the corresponding cobordism groups over Spec(C) for all dimensions of varieties and…
This paper presents a systematic study of coproducts. This is carried out principally, but not exclusively, for finitely generated quasivarieties A that admit a (term) reduct in the variety D of bounded distributive lattices. In this…
We exploit a new theory of duality transformations to construct dual representations of models incompatible with traditional duality transformations. Hence we obtain a solution to the long-standing problem of non-Abelian dualities that…
Natural language semantics has recently sought to combine the complementary strengths of formal and distributional approaches to meaning. More specifically, proposals have been put forward to augment formal semantic machinery with…
In this paper we study the class of modules with fusion and implication based over distributive lattices, or FIDL-modules, for short. We introduce the concepts of FIDL-subalgebra and FIDL-congruence as well as the notions of simple and…
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…
The ordering relation of a bounded distributive lattice L is a (distributive) (0, 1)-sublattice of L \times L. This construction gives rise to a functor \Phi from the category of bounded distributive lattices to itself. We examine the…