Related papers: Conjunctive Table Algebras
We present a number of first- and second-order extensions to SMT theories specifically aimed at representing and analyzing SQL queries with join, projection, and selection operations. We support reasoning about SQL queries with either bag…
In this paper we examine how the notion of algebra of quotients for Lie algebras ties up with the corresponding well-known concept in the associative case. Specifically, we completely characterize when a Lie algebra $Q$ is an algebra of…
The cluster category is a triangulated category introduced for its combinatorial similarities with cluster algebras. We prove that a cluster algebra A of finite type can be realized as a Hall algebra, called the exceptional Hall algebra, of…
Constraint languages that arise from finite algebras have recently been the object of study, especially in connection with the Dichotomy Conjecture of Feder and Vardi. An important class of algebras are those that generate congruence…
In this paper we will first present a generalization of the wedge product of association schemes to table algebras and give a necessary and sufficient condition for a table algebra to be the wedge product of two table algebras. Then we show…
Multi-model databases are designed to store, manage, and query data in various models, such as relational, hierarchical, and graph data, simultaneously. In this paper, we provide a theoretical basis for querying categorical databases. We…
Students in introductory data management courses are often taught how to write queries in SQL. This is a useful and practical skill, but it gives limited insight into how queries are processed by relational database engines. In contrast,…
We interpret augmented racks as a certain kind of multiplicative graphs and show that this point of view is natural for defining rack homology. We also define the analogue of the group algebra for these objects; in particular, we see how…
Every metric symplectic Lie algebra has the structure of a quadratic extension. We give a standard model and describe the equivalence classes on the level of corresponding quadratic cohomology sets. Finally, we give a scheme to classify the…
We describe some connections between three different fields: combinatorics (umbral calculus), functional analysis (linear functionals and operators) and harmonic analysis (convolutions on group-like structures). Systematic usage of…
Algebraic theories, sometimes called equational theories, are syntactic notions given by finitary operations and equations, such as monoids, groups, and rings. There is a well-known category-theoretic treatment of them that algebraic…
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…
Coalgebras for analytic functors uniformly model graph-like systems where the successors of a state may admit certain symmetries. Examples of successor structure include ordered tuples, cyclic lists and multisets. Motivated by goals in…
We develop some foundations of commutative algebra, with a view towards algebraic geometry, in symmetric tensor categories. Most results establish analogues of classical theorems, in tensor categories which admit a tensor functor to some…
We characterize vertex algebras (in a suitable sense) as algebras over a certain graded co-operad. We also discuss some examples and categorical implications of this characterization.
This paper is devoted to the investigation of term-definable connexive implications in substructural logics with exchange and, on the semantical perspective, in sub-varieties of commutative residuated lattices (FLe-algebras). In particular,…
The goal of this paper is to provide a strong integration between constraint modelling and relational DBMSs. To this end we propose extensions of standard query languages such as relational algebra and SQL, by adding constraint modelling…
The Calculus of Conjunctive Queries (CCQ) has foundational status in database theory. A celebrated theorem of Chandra and Merlin states that CCQ query inclusion is decidable. Its proof transforms logical formulas to graphs: each query has a…
Ordered logics and type systems have been used in a variety of applications including computational linguistics, memory allocation, stream processing, logical frameworks, parametricity, and enforcing security protocols. In most…
The notion of an anti-commutative (resp. commutative) rigid superalgebra is a natural generalisation of the notion of a Lie (resp. Jordan) superalgebra. Intuitively rigidity means that small deformations of the product under the structural…