Related papers: Ideal Databases
We define an easily verifiable notion of an atomic formula having uniformly bounded arrays in a structure $M$. We prove that if $T$ is a complete $L$-theory, then $T$ is mutually algebraic if and only if there is some model $M$ of $T$ for…
We derive the algebraic relations of alternating and non-alternating finite harmonic sums up to the sums of depth~6. All relations for the sums up to weight~6 are given in explicit form. These relations depend on the structure of the index…
Several mathematical ideas have been investigated for Quantitative Information Flow. Information theory, probability, guessability are the main ideas in most proposals. They aim to quantify how much information is leaked, how likely is to…
In this paper we study the notion of knowledge from the positions of universal algebra and algebraic logic. We consider first order knowledge which is based on first order logic. We define categories of knowledge and knowledge bases. These…
The class of finitely presented algebras over a field $K$ with a set of generators $a_{1},..., a_{n}$ and defined by homogeneous relations of the form $a_{1}a_{2}... a_{n} =a_{\sigma (1)} a_{\sigma (2)} ... a_{\sigma (n)}$, where $\sigma$…
We give a one-to-one correspondence between ideals in the Steinberg algebra of a Hausdorff ample groupoid $G$, and certain families of ideals in the group algebras of isotropy groups in $G$. This generalises a known ideal correspondence…
Over an arbitrary field of positive characteristic we construct an example of a locally finite variety of Lie algebras which does not have a finite basis of its polynomial identities. As a consequence we construct varieties of Lie algebras…
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…
Formal concept analysis has grown from a new branch of the mathematical field of lattice theory to a widely recognized tool in Computer Science and elsewhere. In order to fully benefit from this theory, we believe that it can be enriched…
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 develop a theory of graph algebras over general fields. This is modeled after the theory developed by Freedman, Lov\'asz and Schrijver in [22] for connection matrices, in the study of graph homomorphism functions over real edge weight…
We explore general intrinsic and extrinsic conditions that allow the transitivity of the relation of being a Lie ideal, in the sense that if a Lie algebra $\mathfrak{h}$ is a subideal of a Lie algebra $\mathfrak{g}$ (i.e. there exist Lie…
This book deals with the theory of generalized algebraic transformations, which is elaborated with the aim to provide a relatively simple theoretical tool that enables an exact treatment of diverse more complex lattice-statistical models.…
We study the Lie algebra structure of the Onsager algebra from the ideal theoretic point of view. A structure theorem of ideals in the Onsager algebra is obtained with the connection to the finite-dimensional representations. We also…
We propose a novel database model whose basic structure is a labeled, directed, acyclic graph with a single root, in which the nodes represent the data sets of an application and the edges represent functional relationships among the data…
Halls of Fame are fascinating constructs. They represent the elite of an often very large amount of entities---persons, companies, products, countries etc. Beyond their practical use as static rankings, changes to them are particularly…
Achieving the goals in the title (and others) relies on a cardinality-wise scanning of the ideals of the poset. Specifically, the relevant numbers attached to the k+1 element ideals are inferred from the corresponding numbers of the…
We present a categorical denotational semantics for a database mapping, based on views, in the most general framework of a database integration/exchange. Developed database category DB, for databases (objects) and view-based mappings…
We begin with a short exposition of the theory of lattice varieties. This includes a description of their orbit structure and smooth locus. We construct a flat cover of the lattice variety and show that it is a complete intersection. We…
Ideals in the ring of power series in three variables can be classified based on algebra structures on their minimal free resolutions. The classification is incomplete in the sense that it remains open which algebra structures actually…