In Formal Concept Analysis, a base for a finite structure is a set of implications that characterizes all valid implications of the structure. This notion can be adapted to the context of Description Logic, where the base consists of a set of concept inclusions instead of implications. In this setting, concept expressions can be arbitrarily large. Thus, it is not clear whether a finite base exists and, if so, how large concept expressions may need to be. We first revisit results in the literature for mining EL bases from finite interpretations. Those mainly focus on finding a finite base or on fixing the role depth but potentially losing some of the valid concept inclusions with higher role depth. We then present a new strategy for mining EL bases which is adaptable in the sense that it can bound the role depth of concepts depending on the local structure of the interpretation. Our strategy guarantees to capture all EL concept inclusions holding in the interpretation, not only the ones up to a fixed role depth.
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.
No abstract
In Formal Concept Analysis, a base for a finite structure is a set of implications that characterizes all valid implications of the structure. This notion can be adapted to the context of Description Logic, where the base consists of a set of concept inclusions instead of implications. In this setting, concept expressions can be arbitrarily large. Thus, it is not clear whether a finite base exists and, if so, how large concept expressions may need to be. We first revisit results in the literature for mining ℰℒ⊥ bases from finite interpretations. Those mainly focus on finding a finite base or on fixing the role depth but potentially losing some of the valid concept inclusions with higher role depth. We then present a new strategy for mining ℰℒ⊥ bases which is adaptable in the sense that it can bound the role depth of concepts depending on the local structure of the interpretation. Our strategy guarantees to capture all ℰℒ⊥ concept inclusions holding in the interpretation, not only the ones up to a fixed role depth. We also consider the case of confident ℰℒ⊥ bases, which requires that some proportion of the domain of the interpretation satisfies the base, instead of the whole domain. This case is useful to cope with noisy data.
Most approaches for repairing description logic (DL) ontologies aim at changing the axioms as little as possible while solving inconsistencies, incoherences and other types of undesired behaviours. As in Belief Change, these issues are often specified using logical formulae. Instead, in the new setting for updating DL ontologies that we propose here, the input for the change is given by a model which we want to add or remove. The main goal is to minimise the loss of information, without concerning with the syntactic structure. This new setting is motivated by scenarios where an ontology is built automatically and needs to be refined or updated. In such situations, the syntactical form is often irrelevant and the incoming information is not necessarily given as a formula. We define general operations and conditions on which they are applicable, and instantiate our approach to the case of ALC-formulae.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.