相关论文: Relational Algebra as non-Distributive Lattice

Relational lattice reduces the set of six classic relational algebra operators to two binary lattice operations: natural join and inner union. We give an introduction to this theory with emphasis on formal algebraic laws. New results…

Relational Lattice is a succinct mathematical model for Relational Algebra. It reduces the set of six classic relational algebra operators to two: natural join and inner union. In this paper we push relational lattice theory in two…

Relational lattice is a formal mathematical model for Relational algebra. It reduces the set of six classic relational algebra operators to two: natural join and inner union. We continue to investigate Relational lattice properties with…

On an infinite set some closure operators are finitary (algebraic) while others are not. We can generalize this idea for a complete algebraic lattice letting the compact elements act as the finite sets. With this in mind, we will consider…

By considering generalized logarithm and exponential functions used in nonextensive statistics, the four usual algebraic operators : addition, subtraction, product and division, are generalized. The properties of the generalized operators…

The natural join and the inner union operations combine relations of a database. Tropashko and Spight [24] realized that these two operations are the meet and join operations in a class of lattices, known by now as the relational lattices.…

Non-classical generalizations of classical modal logic have been developed in the contexts of constructive mathematics and natural language semantics. In this paper, we discuss a general approach to the semantics of non-classical modal…

The aim of this paper is to show that even if the natural algebraic semantic for modal (normal) logic is modal algebra, the more general class of subordination algebras (roughly speaking, the non symmetric contact algebras) is adequate too…

We employ the theory of canonical extensions to study residuation algebras whose associated relational structures are functional, i.e., for which the ternary relations associated to the expanded operations admit an interpretation as…

We consider all 16 unary operations that, given a homogeneous binary relation R, define a new one by a boolean combination of xRy and yRx. Operations can be composed, and connected by pointwise-defined logical junctors. We consider the…

Disjoint union is a partial binary operation returning the union of two sets if they are disjoint and undefined otherwise. A disjoint-union partial algebra of sets is a collection of sets closed under disjoint unions, whenever they are…

This paper presents a graded hierarchy or chain of binary operations on the reals and the complex numbers. The operations are related distributively in the sense that any one of them distributes over the next lower operation in the chain.…

Lattice theoretical generalizations of some classical linear algebra results are formulated. A vector space is replaced by its subspace lattice and a linear map is replaced by the induced lattice map. This map is a complete join…

For a complete lattice $L$ and a relational structure $\mathfrak{X}=(X,(R_i)_I)$, we introduce the convolution algebra $L^{\mathfrak{X}}$. This algebra consists of the lattice $L^X$ equipped with an additional $n_i$-ary operation $f_i$ for…

We exhibit an adjunction between a category of abstract algebras of partial functions and a category of set quotients. The algebras are those atomic algebras representable as a collection of partial functions closed under relative…

A finite-dimensional unital and associative algebra over $\mathbb{R}$, or what we shall call simply "an algebra" in this paper for short, generalities the construction by which we derive the complex numbers by "adjoining an element $i$" to…

Quantum physics has revealed many interesting formal properties associated with the algebra of two operators, A and B, satisfying the partial commutation relation AB-BA=1. This study surveys the relationships between classical combinatorial…

We construct a completely normal bounded distributive lattice D in which for every pair (a, b) of elements, the set {x $\in$ D | a $\le$ b $\lor$ x} has a countable coinitial subset, such that D does not carry any binary operation -…

The natural join and the inner union combine in different ways tables of a relational database. Tropashko [18] observed that these two operations are the meet and join in a class of lattices-called the relational lattices- and proposed…

We present module theory and linear maps as a powerful generalised and computationally efficient framework for the relational data model, which underpins today's relational database systems. Based on universal constructions of modules we…