Modularity in belief change of description logic bases

Abstract

Ontologies written in OWL and OWL 2 are one of the most prominent tools in Knowledge Representation nowadays. They allow the sharing of knowledge of a domain unambiguously and operate with implicit knowledge using reasoning algorithms. However, ontologies can become large and very complex, difficulting their maintenance and evolution. One complicating factor is that a small change can trigger unexpected and unwanted consequences.Solutions to sound maintenance have emerged separately in Belief Change and Ontology Repair.Despite having distinct views, proposals in both fields often rely on the Description Logics, which underpin OWL and OWL 2. Hence, the approaches from both fields for repairing ontologies are very similar at the algorithmic level. Consequently, both areas need to address the high complexity of the debugging problem and cope with the exponential number of correct outcomes.There are studies in Ontology Repair which use modularity techniques to extract smaller subsets of the ontology which are sufficient to fix a particular consequence. Still, the effect of modules on the Belief Change framework is poorly understood: either the postulates or the mechanisms which select the final result might change when a module replaces the input. Also, the impact on computational performance was only assessed in small corpora and with few variations in parameters. Further, the number of outcomes is still exponential, and existing solutions rarely provide means to mitigate this issue.In this direction, this thesis provides a clearer understanding of the effects of modularity in the theoretical framework that guarantees rational (sound) changes. Also, it evaluates the performance impact of modularity empirically using locality-based modules in a broader setting. Additionally, it also investigates how modules can aid users to filter and select the best results efficiently. A category of modules is identified for which the postulates from Belief Change remain the same, and under mild conditions, the result is unchanged. The analysis of experimental data shows that modules are beneficial for performance, often displaying gains of orders of magnitude. Further, the methods proposed to aid in the selection of repairs are shown to be competitive with existing methods.

Quantification in description logics of typicality

“…On the one hand, there are no useful benchmarks against which to test possible implementations of the existing methods. Hence, researchers must develop artificial ones, as in [Bon+15b] and [Gui20]. On the other hand, the lack of implementations is a problem in itself.…”