Fitting Ontologies and Constraints to Relational Structures
This work addresses foundational challenges in knowledge representation and database theory for researchers and practitioners dealing with ontology learning and constraint inference.
The paper tackles the problem of fitting ontologies and constraints, such as description logics and tuple-generating dependencies, to finite relational structures with positive and negative examples, by determining computational complexity, designing algorithms, and analyzing ontology size. It also investigates constructing finite bases for these constraints, finding they exist for some languages but not others.
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.