Fitting Ontologies and Constraints to Relational Structures

TL;DR

This paper investigates the computational complexity and algorithms for fitting ontologies and constraints, such as description logics and TGDs, to relational data structures, and explores the existence of finite bases for these fits.

Contribution

It provides a detailed complexity analysis, algorithmic solutions, and size bounds for fitting ontologies and constraints, and characterizes when finite bases exist.

Findings

Finite bases exist for certain description logics and dependencies.

Complexity results are established for various classes of constraints.

Algorithms and bounds are provided for fitting ontologies to data structures.

Abstract

We study the problem of fitting ontologies and constraints to positive and negative examples that take the form of a finite relational structure. As ontology and constraint languages, we consider the description logics $\mathcal{E\mkern-2mu L}$ and $\mathcal{E\mkern-2mu LI}$ as well as several classes of tuple-generating dependencies (TGDs): full, guarded, frontier-guarded, frontier-one, and unrestricted TGDs as well as inclusion dependencies. We pinpoint the exact computational complexity, design algorithms, and analyze the size of fitting ontologies and TGDs. We also investigate the related problem of constructing a finite basis of concept inclusions / TGDs for a given set of finite structures. While finite bases exist for $\mathcal{E\mkern-2mu L}$, $\mathcal{E\mkern-2mu LI}$, guarded TGDs, and inclusion dependencies, they in general do not exist for full, frontier-guarded and frontier-one TGDs.