Related papers: An algebraic approach to weak and delay bismulatio…
This paper presents State Algebra, a novel framework designed to represent and manipulate propositional logic using algebraic methods. The framework is structured as a hierarchy of three representations: Set, Coordinate, and Row…
The category of unital (unbounded) dg cocommutative coalgebras over a field of characteristic zero is provided with a structure of simplicial closed model category. This generalizes the model structure defined by Quillen in 1969 for…
The modelling, specification and study of the semantics of concurrent reactive systems have been interesting research topics for many years now. The aim of this thesis is to exploit the strengths of the (co)algebraic framework in modelling…
We introduce three general compositionality criteria over operational semantics and prove that, when all three are satisfied together, they guarantee weak bisimulation being a congruence. Our work is founded upon Turi and Plotkin's…
We investigate the extent to which the weak equivalences in a model category can be equipped with algebraic structure. We prove, for instance, that there exists a monad T such that a morphism of topological spaces admits T-algebra structure…
The aim of this paper is to define and study the involutive and weakly involutive quantum B-algebras. We prove that any weakly involutive quantum B-algebra is a quantum B-algebra with pseudo-product. As an application, we introduce and…
We develop a notion of cell decomposition suitable for studying weak p- adic structures (reducts of p-adic fields where addition and multiplication are not (everywhere) definable). As an example, we apply this to a language with restricted…
The foundational character of certain algebraic structures as Boolean algebras and Heyting algebras is rooted in their potential to model classical and constructive logic, respectively. In this paper we discuss the contributions of…
We introduce and study bisimulations for coalgebras on Stone spaces [14]. Our notion of bisimulation is sound and complete for behavioural equivalence, and generalizes Vietoris bisimulations [4]. The main result of our paper is that…
We revisit our earlier work on the representation of quantum systems as Chu spaces, and investigate the use of coalgebra as an alternative framework. On the one hand, coalgebras allow the dynamics of repeated measurement to be captured, and…
We study general properties of multipliers and weak multipliers of algebras. We apply the results to determine the (weak) multipliers of associative algebras and zeropotent algebras of dimension 3 over an algebraically closed field.
We aim at studying collections of algebraic structures defined over a commutative ring and investigating the complexity of significant constructions carried out on these objects. The assignment of measures of size, via a multiplicity…
If A is a finite-dimensional symmetric algebra, then it is well-known that the only silting complexes in $\mathrm{K^b}(\mathrm{proj}A)$ are the tilting complexes. In this note we investigate to what extent the same can be said for weakly…
The purpose of this paper is to introduce an algebraic cohomology and formal deformation theory of left alternative algebras. Connections to some other algebraic structures are given also.
Earlier we presented a method to decompose modal formulas for processes with the internal action $\tau$, and congruence formats for branching and $\eta$-bisimilarity were derived on the basis of this decomposition method. The idea is that a…
In this paper, weakly homogeneous generalized functions in the special Colombeau algebras are determined up to equality in the sense of generalized distributions. This yields characterizations that are formally similar to distribution…
We present a comprehensive programme analysing the decomposition of proof systems for non-classical logics into proof systems for other logics, especially classical logic, using an algebra of constraints. That is, one recovers a proof…
The motivation of this paper is to construct a deformation theory of coderivations of coassociative coalgebras. We introduce a notion of a Coder pair, that is, a coassociative coalgebra with a coderivation. Then we define a proper…
Bialgebrae provide an abstract framework encompassing the semantics of different kinds of computational models. In this paper we propose a bialgebraic approach to the semantics of logic programming. Our methodology is to study logic…
In this article, we study short exact sequences of finitary 2-representations of a weakly fiat 2-category. We provide a correspondence between such short exact sequences with fixed middle term and coidempotent subcoalgebras of a coalgebra…