Related papers: On matrices and $K$-relations
Linear algebra algorithms often require some sort of iteration or recursion as is illustrated by standard algorithms for Gaussian elimination, matrix inversion, and transitive closure. A key characteristic shared by these algorithms is that…
We investigate the expressive power of $\mathsf{MATLANG}$, a formal language for matrix manipulation based on common matrix operations and linear algebra. The language can be extended with the operation $\mathsf{inv}$ of inverting a matrix.…
Due to the importance of linear algebra and matrix operations in data analytics, there is significant interest in using relational query optimization and processing techniques for evaluating (sparse) linear algebra programs. In particular,…
We generalize Kracht's theory of internal describability from classical modal logic to the family of all logics canonically associated with varieties of normal lattice expansions (LE algebras). We work in the purely algebraic setting of…
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…
One of the most promising applications of mathematical knowledge management is search: Even if we restrict attention to the tiny fragment of mathematics that has been formalized, the amount exceeds the comprehension of an individual human.…
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…
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 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…
In spatial databases, incompatibilities often arise due to different choices of origin or unit of measurement (e.g., centimeters versus inches). By representing and querying the data in an affine-invariant manner, we can avoid these…
We present an example of a quadratic algebra given by three generators and three relations, which is automaton (the set of normal words forms a regular language) and such that its ideal of relations does not possess a finite Gr\"obner basis…
We present a simple technique for semantic, open logical relations arguments about languages with recursive types, which, as we show, follows from a principled foundation in categorical semantics. We demonstrate how it can be used to give a…
A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This…
We present an algebraic framework for interacting extended quantum systems to study complex phenomena characterized by the coexistence and competition of different states of matter. We start by showing how to connect different…
We study the expressive power of the LARA language -- a recently proposed unified model for expressing relational and linear algebra operations -- both in terms of traditional database query languages and some analytic tasks often performed…
Algebraic quantum field theory, or AQFT for short, is a rigorous analysis of the structure of relativistic quantum mechanics. It is formulated in terms of a net of operator algebras indexed by regions of a Lorentzian manifold. In several…
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,…
We present a system of relational syllogistic, based on classical propositional logic, having primitives of the following form: Some A are R-related to some B; Some A are R-related to all B; All A are R-related to some B; All A are…
Given an associative multiplication in matrix algebra compatible with the usual one or, in other words, linear deformation of matrix algebra, we construct a solution to the classical Yang-Baxter equation. We also develop a theory of such…
A number of models of linear logic are based on or closely related to linear algebra, in the sense that morphisms are "matrices" over appropriate coefficient sets. Examples include models based on coherence spaces, finiteness spaces and…