Related papers: An algebraic analysis of implication in non-distri…
We introduce here the notion of syntactic lattice algebra which is an analogy of the syntactic monoid and of the syntactic semiring. We present a unified approach to get those three structures.
We study different representation theorems for various reducts of Heyting polyadic algebras. Superamalgamation is proved for several (natural reducts) and our results are compared to the finitizability problem in classical algebraic logic…
The goal of this paper is to present some results and (more importantly) state a number of conjectures suggesting that the representation theory of symplectic reflection algebras for wreath products categorifies certain structures in the…
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…
In this Master of Science Thesis I introduce geometric algebra both from the traditional geometric setting of vector spaces, and also from a more combinatorial view which simplifies common relations and operations. This view enables us to…
The Weihrauch degrees and strong Weihrauch degrees are partially ordered structures representing degrees of unsolvability of various mathematical problems. Their study has been widely applied in computable analysis, complexity theory, and…
In a recent work we have shown how to construct an information algebra of coherent sets of gambles defined on general possibility spaces. Here we analyze the connection of such an algebra with the set algebra of subsets of the possibility…
A subalgebra $\mathcal{A}$ of a $C^*$-algebra $\mathcal{M}$ is logmodular (resp. has factorization) if the set $\{a^*a; a\text{ is invertible with }a,a^{-1}\in\mathcal{A}\}$ is dense in (resp. equal to) the set of all positive and…
This paper reveals a categorical equivalence connecting two distinct quantum logic structures. The first is the orthomodular lattice, an algebraic system designed to formalize the properties of quantum systems. The second is a finitary…
Nonlinear $sl(2)$ algebras subtending generalized angular momentum theories are studied in terms of undeformed generators and bases. We construct their unitary irreducible representations in such a general context. The linear $sl(2)$-case…
Motivated by Gentzen disjunction elimination rule in his Natural Deduction calculus and reading inequalities with meet in a natural way, we conceive a notion of distributivity for join-semilattices. We prove that it is equivalent to a…
An involutive Stone algebra (IS-algebra) is a structure that is simultaneously a De Morgan algebra and a Stone algebra (i.e. a pseudo-complemented distributive lattice satisfying the well-known Stone identity ~xv~~x=1). IS-algebras have…
We introduce a class of equivalences, which we call generalized semi-infinite Hecke equivalences, between certain categories of representations of graded associative algebras which appear in the setting of semi-infinite cohomology for…
We develop a new duality for distributive and implicative meet semi-lattices. For distributive meet semi-lattices our duality generalizes Priestley's duality for distributive lattices and provides an improvement of Celani's duality. Our…
We introduce a generalization, called a skew Clifford algebra, of a Clifford algebra, and relate these new algebras to the notion of graded skew Clifford algebra that was defined in 2010. In particular, we examine homogenizations of skew…
Let $\cH$ be the one-parameter Hecke algebra associated to a finite Weyl group $W$, defined over a ground ring in which ``bad'' primes for $W$ are invertible. Using deep properties of the Kazhdan--Lusztig basis of $\cH$ and Lusztig's…
We show that the variety of symmetric implication algebras is generated from cubic implication algebras and Boolean algebras. We do this by developing the notion of a locally symmetric implication algebra that has properties similar to…
Mitsch's natural partial order on the semigroup of binary relations is here characterised by equations in the theory of relation algebras. The natural partial order has a complex relationship with the compatible partial order of inclusion,…
Perfect paradefinite algebras are De Morgan algebras expanded with an operation that allows for the full behavior of classical negation to be restored. They form a variety that is term-equivalent to the variety of involutive Stone algebras.…
Nonrigid mathematical structures may no longer form usual Eilenberg - Mac Lane categories, but more general ones, as illustrated by pseudo-topologies. A rather general concept of pseudo-topology was used in constructing differential…