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 directions. First, we uncover a pair of complementary lattice operators, and organize the model into a bilattice of four operations and four distinguished constants. We take a notice a peculiar way bilattice symmetry is broken. Then, we give axiomatic introduction of unary negation operation and prove several laws, including double negation and De Morgan. Next we reduce the model back to two basic binary operations and twelve axioms, and exhibit a convincing argument that the resulting system is complete in model-theoretic sense. The final parts of the paper casts relational lattice perspective onto database dependency theory and into cylindric algebras.
Rules complement and extend ontologies on the Semantic Web. We refer to these rules as onto-relational since they combine DL-based ontology languages and Knowledge Representation formalisms supporting the relational data model within the tradition of Logic Programming and Deductive Databases. Rule authoring is a very demanding Knowledge Engineering task which can be automated though partially by applying Machine Learning algorithms. In this chapter we show how Inductive Logic Programming (ILP), born at the intersection of Machine Learning and Logic Programming and considered as a major approac…
We propose a new formalism for specifying and reasoning about problems that involve heterogeneous "pieces of information" -- large collections of data, decision procedures of any kind and complexity and connections between them. The essence of our proposal is to lift Codd's relational algebra from operations on relational tables to operations on classes of structures (with recursion), and to add a direction of information propagation. We observe the presence of information propagation in several formalisms for efficient reasoning and use it to express unary negation and operations used in grap…
Normalized relations extended with inherited attributes can be more faithful to reality and support logical navigation free queries, properties available at present only through specific views. Adding inherited attributes can be nonetheless always less procedural than to define any such views. Present schemes should even typically suffice for relations with foreign keys. Implementing extended relations on popular DBSs appears also simple. Relational model should evolve accordingly, for benefit of likely millions of DBAs, clients, developers.
The logic of nulls in databases has been subject of investigation since their introduction in Codd's Relational Model, which is the foundation of the SQL standard. We show a logical characterisation of a first-order fragment of SQL with null values, by first focussing on a simple extension with null values of standard relational algebra, which captures exactly the SQL fragment, and then proposing two different domain relational calculi, in which the null value is a term of the language but it does not appear as an element of the semantic interpretation domain of the logics. In one calculus, a …
We show that there is a query expressible in first-order logic over the reals that returns, on any given semi-algebraic set A, for every point a radius around which A is conical. We obtain this result by combining famous results from calculus and real algebraic geometry, notably Sard's theorem and Thom's first isotopy lemma, with recent algorithmic results by Rannou.
Our aim in this paper is to point out a surprising formal connection, between two topics which seem on face value to have nothing to do with each other: relational database theory, and the study of non-locality and contextuality in the foundations of quantum mechanics. We shall show that there is a remarkably direct correspondence between central results such as Bell's theorem in the foundations of quantum mechanics, and questions which arise naturally and have been well-studied in relational database theory.
Towards Foundation Models for Relational Databases with Language Models and Graph Neural Networks
University of Stuttgart, Stuttgart, Germany（斯图加特大学）；Internet Science Research Group, University of Southampton, Southampton, United Kingdom（互联网科学研究组，南安普顿大学）
We study the data transformation capabilities associated with schemas that are presented by directed multi-graphs and path equations. Unlike most approaches which treat graph-based schemas as abbreviations for relational schemas, we treat graph-based schemas as categories. A schema $S$ is a finitely-presented category, and the collection of all $S$-instances forms a category, $S$-inst. A functor $F$ between schemas $S$ and $T$, which can be generated from a visual mapping between graphs, induces three adjoint data migration functors, $Σ_F:S$-inst$\to T$-inst, $Π_F: S$-inst $\to T$-inst, and $Δ…
Alloy is a lightweight modeling formalism based on relational algebra. In prior work with Fisler, Giannakopoulos, Krishnamurthi, and Yoo, we have presented a tool, Alchemy, that compiles Alloy specifications into implementations that execute against persistent databases. The foundation of Alchemy is an algorithm for rewriting relational algebra formulas into code for database transactions. In this paper we report on recent progress in improving the robustness and efficiency of this transformation.
Relational In-Context Learning via Synthetic Pre-training with Structural Prior
Institute for Artificial Intelligence, Peking University（北京大学人工智能研究院）；University of Illinois at Urbana-Champaign（伊利诺伊大学香槟分校）；Institute of Computing Technology, Beijing University of Post（北京邮电大学计算机学院）；State Key Laboratory of General Artificial Intelligence（通用人工智能国家重点实验室）
