Practical Reasoning for Defeasible Description Logics

Abstract

I, , declare that:1. The research reported in this dissertation, except where otherwise indicated, is my original research.2. This dissertation has not been submitted for any degree or examination at any other university. 5. This dissertation does not contain text, graphics or tables copied and pasted from the Internet, unless specifically acknowledged, and the source being detailed in the dissertation and in the References section.

DDLV: A System for rational preferential reasoning for datalog

“…Figure 3 shows the ranking compilation time for DIP for each of 10 groups of defeasible ontologies, while Figure 4 shows the ranking compilation time of DDLV for the 10 groups of defeasible Datalog programs. Moodley used percentile plots because they give a good general picture of the performance and reveal outliers quickly (Moodley, 2015). For example, if the value for the P90 bar is 40 seconds then it means that 90% of the ontologies (in the case of DIP) or programs(in the case of DDLV) could have their ranking computed in 40 seconds or less.…”

“…Note that the vertical scale for Figure 3 is logarithmic whereas the vertical scale for Figure 4 is linear. (Moodley, 2015) Computing the ranking is the greatest bottleneck with this approach. Once the ranking has been computed, defeasible entailment checks can be performed very quickly.…”

“…The KLM approach has been successfully lifted to Description Logics (Casini & Straccia, 2010) as a way to extend the Description Logic language ALC with nonmonotonic reasoning capabilities. A practical defeasible reasoning system (Moodley, 2015) using the KLM approach has even been implemented in the form of a plugin for Protégé, an ontology engineering program.…”

Algorithmic definitions for KLM-style defeasible disjunctive Datalog

“…Lehmann and Magidor's definition of rationality (1992) is used extensively in the literature and we use it throughout the paper. The framework has been discussed at length in the literature for propositional logic (Kraus et al, 1990;Lehmann, 1995;Lehmann & Magidor, 1992) and description logics (Casini et al, 2014;Casini et al, 2013;Moodley, 2015;Straccia Morris, M., Ross, T., and Meyer, T. (2020). Algorithmic definitions for KLM-style defeasible disjunctive Datalog.…”

Defeasible Reasoning in 𝒮ℛ𝒪ℰℒ: from Rational Entailment to Rational Closure

“…The rational closure of a knowledge base has been introduced by Lehmann and Magidor [43] to allow for stronger inferences with respect to preferential and rational entailment, and several constructions of rational closure have been proposed for ALC [14,16,13,32,46]. Such constructions are defined for knowledge bases containing strict or defeasible inclusions and, for the construction in [32], which allows for defeasible inclusions of the form T(C) ⊑ D (where C and D are ALC concepts), minimal canonical ranked models have been shown to provide a semantic characterization of rational closure for ALC, thus generalizing to DLs the canonical model result in [43].…”