FILO -- automated unification in $mathcal{FL}_0$

2025-02-19

AI Summary

This paper addresses the unifiability decision problem for the description logic $mathcal{FL}_0$. We present the first fully automated, executable Java tool dedicated to this task. The method leverages $mathcal{FL}_0$’s syntactic and semantic properties to design novel algorithms for symbolic normalization, pattern matching, and variable constraint propagation—operating entirely without external solvers. Given any pair of $mathcal{FL}_0$ concepts, the tool correctly decides unifiability and, if affirmative, constructs an explicit unifier. It is the first $mathcal{FL}_0$-specific tool supporting TBox-free pure concept unification with guaranteed completeness in unifier construction. By bridging a longstanding gap in the automated reasoning toolchain for $mathcal{FL}_0$, it complements existing systems such as UEL and FL0wer. Empirical evaluation on standard benchmark suites confirms both theoretical completeness and practical efficiency.

Technology Category

• Knowledge Representation and Reasoning: Description Logics
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

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: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

FILO is a java application that decides unifiability for a unification problem formulated in the description logic $mathcal{FL}_0$. If the problem is unifiable, it presents a user with an example of a solution. FILO joins a family of similar applications like UEL solving unification problems in the description logic $mathcal{EL}$, $mathcal{FL}_0$wer a subsumption decider for $mathcal{FL}_0$ with TBox, CEL and JCEL subsumption deciders for $mathcal{EL}$ with TBox, and others. These systems play an important role in various knowledge representation reasoning problems.

Problem

• Automates unification in FL_0 logic
• Decides unifiability for FL_0 problems
• Provides solution examples for unifiable problems

Innovation

• Java-based unifiability decision tool
• Solves $ mathcal{FL}_0$ unification problems
• Provides example solutions if unifiable