Related papers: Algebraic Data Integration
Conjunctive table algebras are introduced and axiomatically characterized. A conjunctive table algebra is a variant of SPJR algebra (a weaker form of relational algebra), which corresponds to conjunctive queries with equality. The table…
The integration of knowledge extracted from different models described by domain experts or from models generated by machine learning algorithms is strongly conditioned by the lack of an appropriated framework to specify and integrate…
In quantum mechanics, one can express the evolution operator and other quantities in terms of functional integrals. The main goal of this paper is to prove corresponding results in the geometric approach to quantum theory. We apply these…
Several tasks in artificial intelligence require to be able to find models about knowledge dynamics. They include belief revision, fusion and belief merging, and abduction. In this paper we exploit the algebraic framework of mathematical…
We present a methodology for integrating functional data into deep densely connected feed-forward neural networks. The model is defined for scalar responses with multiple functional and scalar covariates. A by-product of the method is a set…
Form factor sequences of an integrable QFT can be defined axiomatically as solutions of a system of recursive functional equations, known as ``form factor equations''. We show that their solution can be replaced with the study of the…
Algebraic datatypes, and among them lists and trees, have attracted a lot of interest in automated reasoning and Satisfiability Modulo Theories (SMT). Since its latest stable version, the SMT-LIB standard defines a theory of algebraic…
A Datalog program can be viewed as a syntactic specification of a functor from database instances over some schema to database instances over another schema. The same holds more generally for $\exists$Datalog. We establish large classes of…
This paper provides a general account of the notion of recursive program schemes, studying both uninterpreted and interpreted solutions. It can be regarded as the category-theoretic version of the classical area of algebraic semantics. The…
We consider a core language of graph queries. These queries are seen as formulas to be solved with respect to graph-oriented databases. For this purpose, we first define a graph query algebra where some operations over graphs and sets of…
Unstructured enterprise data such as reports, manuals and guidelines often contain tables. The traditional way of integrating data from these tables is through a two-step process of table detection/extraction and mapping the table layouts…
Lambda-S is an extension to first-order lambda calculus unifying two approaches of non-cloning in quantum lambda-calculi. One is to forbid duplication of variables, while the other is to consider all lambda-terms as algebraic linear…
We present a systematic, algebraically based, design methodology for efficient implementation of computer programs optimized over multiple levels of the processor/memory and network hierarchy. Using a common formalism to describe the…
In this paper we propose an algebraic formalization of connectors in the quantitative setting, in order to address their non-functional features in architectures of component-based systems. We firstly present a weighted Algebra of…
Tabular data, a fundamental data format in machine learning, is predominantly utilized in competitions and real-world applications. The performance of tabular models--such as gradient boosted decision trees and neural networks--can vary…
We introduce an automated method for structuring textual data into a model-agnostic schema, enabling alignment with any database model. It generates both a schema and its instance. Initially, textual data is represented as semantically…
This paper uses typed linear algebra (LA) to represent data and perform analytical querying in a single, unified framework. The typed approach offers strong type checking (as in modern programming languages) and a diagrammatic way of…
Recent advances in large language models (LLMs) have greatly improved Text-to-SQL performance for single-table queries. But, it remains challenging in multi-table databases due to complex schema and relational operations. Existing methods…
The first-order logical environment FOLE [5] provides a rigorous and principled approach to distributed interoperable first-order information systems. FOLE has been developed in two forms: a classification form and an interpretation form.…
Main contribution of this paper is an investigation of expressive power of the database category DB. An object in this category is a database-instance (set of n-ary relations). Morphisms are not functions but have complex tree structures…