相关论文: On Enforcing Satisfiable, Coherent, and Minimal Se…

This paper rigorously and concisely defines, in the context of our (Elementary) Mathematical Data Model ((E)MDM), the mathematical concepts of self-map, composite mapping, totality, one-to-oneness, non-primeness, ontoness, bijectivity,…

We present a pseudocode algorithm for translating our (Elementary) Mathematical Data Model schemes into relational ones and associated sets of non-relational constraints, used by MatBase, our intelligent data and knowledge base management…

Presented are algorithms for enforcing function diagram commutativity and anti-commutativity database constraints, using the database software application constraint-driven design and development methodology, in the realm of the…

This paper presents a pseudocode algorithm for translating (Elementary) Mathematical Data Model ((E)MDM) schemes into Entity-Relationship data models. We prove that this algorithm is linear, sound, complete, and semi-optimal. As an example,…

Existence constraints were defined in the Relational Data Model, but, unfortunately, are not provided by any Relational Database Management System, except for their NOT NULL particular case. Our (Elementary) Mathematical Data Model extended…

Homogeneous binary function products are often encountered in the sub-universes modeled by databases, from genealogical trees to sports, from education to healthcare, etc. Their properties must be discovered and enforced by the software…

This paper presents a pseudocode algorithm for translating Entity-Relationship data models into (Elementary) Mathematical Data Model schemes. We prove that this algorithm is linear, sound, complete, and optimal. As an example, we apply this…

This research paper introduces two new constraint types and four subtypes of database constraints added to our (Elementary) Mathematical Data Model, which are the duals of the existence and non-existence ones. They are formally defined,…

MatBase is a prototype intelligent data and knowledge base management system based on the Relational, Entity-Relationship, and (Elementary) Mathematical Data Models. The latter distinguishes itself especially by its rich panoply of…

This paper presents the current version of our (Elementary) Mathematical Data Model ((E)MDM), which is based on the na\"ive theory of sets, relations, and functions, as well as on the first-order predicate calculus with equality. Many…

This paper defines a constraint-based model dedicated to multidimensional databases. The model we define represents data through a constellation of facts (subjects of analyse) associated to dimensions (axis of analyse), which are possibly…

The concept of matching dependencies (mds) is recently pro- posed for specifying matching rules for object identification. Similar to the functional dependencies (with conditions), mds can also be applied to various data quality…

Implicational bases (IBs) are a common representation of finite closure systems and lattices, along with meet-irreducible elements. They appear in a wide variety of fields ranging from logic and databases to Knowledge Space Theory.…

Euclidean distance matrices (EDM) are matrices of squared distances between points. The definition is deceivingly simple: thanks to their many useful properties they have found applications in psychometrics, crystallography, machine…

Separate programming models for data transformation (declarative) and computation (procedural) impact programmer ergonomics, code reusability and database efficiency. To eliminate the necessity for two models or paradigms, we propose a…

We consider the problem of embedding entities and relations of knowledge bases in low-dimensional vector spaces. Unlike most existing approaches, which are primarily efficient for modeling equivalence relations, our approach is designed to…

Relational properties arise in many settings: relating two versions of a program that use different data representations, noninterference properties for security, etc. The main ingredient of relational verification, relating aligned pairs…

Datasets often contain values that naturally reside in a metric space: numbers, strings, geographical locations, machine-learned embeddings in a Euclidean space, and so on. We study the computational complexity of repairing inconsistent…

In view of the paradigm shift that makes science ever more data-driven, in this paper we consider deterministic scientific hypotheses as uncertain data. In the form of mathematical equations, hypotheses symmetrically relate aspects of the…

Deep neural networks trained through end-to-end learning have achieved remarkable success across various domains in the past decade. However, the end-to-end learning strategy, originally designed to minimize predictive loss in a black-box…