Related papers: Unsharp residuation in effect algebras
An order theoretic and algebraic framework for the extended real numbers is established which includes extensions of the usual difference to expressions involving $-\infty$ and/or $+\infty$, so-called residuations. Based on this,…
Let $A$ be an additively cancellative semialgebra over an additively cancellative semifield $K$ as defined in [9]. For a given partial action $\alpha$ of a group $G$ on an algebra, the associativity of partial skew group ring together with…
We give a definition of representability for distributive quasi relation algebras (DqRAs). These algebras are a generalisation of relation algebras and were first described by Galatos and Jipsen (2013). Our definition uses a construction…
In this paper, we introduce the class of finitely semi-graded algebras which extends the connected graded algebras finitely generated in degree one. The Koszul behavior of finitely semi-graded algebras is investigated by the distributivity…
In a recent work Foulis and Pulmannov\' a \cite{Foulis2012} studied the logical connectives in lattice effect algebras. In this paper we extend their study and investigate further the logical calculus for which the lattice effect algebras…
We analyze loop-induced group-like symmetries in theories where fields are labeled by basis elements of a fusion algebra constructed from the conjugacy classes of finite groups. Although the fusion rules for conjugacy classes are in general…
We introduce a notion of residual derivative for elements of a preordered set, a construction that generalizes both the Frattini subgroup in algebra and the Cantor-Bendixson derivative in T1 topological spaces. For dual algebraic coframes…
A decomposition space (also called 2-Segal space) is a simplicial object satisfying an exactness condition weaker than the Segal condition: just as the Segal condition expresses composition, the new condition expresses decomposition. It is…
Algebraic effects are computational effects that can be represented by an equational theory whose operations produce the effects at hand. The free model of this theory induces the expected computational monad for the corresponding effect.…
In this paper we extend our previous results on sets of graded attribute implications with witnessed non-redundancy. We assume finite residuated lattices as structures of truth degrees and use arbitrary idempotent truth-stressing linguistic…
Our basic structure is a finite-dimensional complex Hilbert space $H$. We point out that the set of effects on $H$ form a convex effect algebra. Although the set of operators on $H$ also form a convex effect algebra, they have a more…
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…
In [1] we introduced the notion of 'structured space', i.e. a space which locally resembles various algebraic structures. In [2] and [3] we studied some cohomology theories related to these space. In this paper we continue in this…
The aim of the present paper is to extend the concept of a congruence from lattices to posets. We use an approach different from that used by the first author and V. Sn\'a\v{s}el. By using our definition we show that congruence classes are…
The residuated lattices form one of the most important algebras of fuzzy logics and have been heavily studied by people from various different points of view. Sheaf presentations provide a topological approach to many algebraic structures.…
Interactions and effect aliasing are among the fundamental concepts in experimental design. In this paper, some new insights and approaches are provided on these subjects. In the literature, the "de-aliasing" of aliased effects is deemed to…
We examine properties of generic automorphisms of the random poset, with the goal of explicitly characterizing them. We associate to each automorphism an auxiliary first-order structure, consisting of the random poset equipped with an…
We study the algebraic theory of computable functions, which can be viewed as arising from possibly non-halting computer programs or algorithms, acting on some state space, equipped with operations of composition, {\em if-then-else} and…
We refine and advance the study of the local structure of idempotent finite algebras started in [A.Bulatov, The Graph of a Relational Structure and Constraint Satisfaction Problems, LICS, 2004]. We introduce a graph-like structure on an…
Every partial applicative structure gives rise to an indexed binary relation, that is a contravariant functor from the category of sets to the category of sets endowed with binary relations and maps preserving them. In this paper we…