Fitting Ontologies and Constraints to Relational Structures

2025-08-11

AI Summary

This paper investigates the ontology and constraint fitting problem over finite relational structures (positive/negative examples), focusing on description logics $mathcal{EL}$ and $mathcal{ELI}$, and classes of tuple-generating dependencies (TGDs)—including guarded, frontier-guarded, and inclusion dependencies. Methodologically, it establishes precise computational complexity characterizations (e.g., PTIME-, NP-, and 2EXPTIME-completeness) for fitting across these formalisms and devises polynomial- or exponential-time algorithms. It proves that guarded TGDs admit finite universal models (finite bases) over finite structures, whereas arbitrary TGDs generally do not. Furthermore, it establishes finite-basis existence results for concept inclusion rules in $mathcal{EL}$ and $mathcal{ELI}$. These contributions provide foundational theoretical guarantees and algorithmic tools for example-driven, automated knowledge base construction.

Technology Category

• Knowledge Representation and Reasoning: Description Logics
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Machine Learning: Statistical Relational/Logic Learning

Application Category

• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

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 $mathcal{Emkern-2mu L}$ and $mathcal{Emkern-2mu LI}$ 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 $mathcal{Emkern-2mu L}$, $mathcal{Emkern-2mu LI}$, guarded TGDs, and inclusion dependencies, they in general do not exist for full, frontier-guarded and frontier-one TGDs.

Problem

• Fitting ontologies and constraints to relational examples
• Analyzing computational complexity and designing algorithms
• Investigating existence of finite bases for logical languages

Innovation

• Description logics for ontology fitting
• Tuple-generating dependencies constraints analysis
• Computational complexity and algorithm design