On rational entailment for Propositional Typicality Logic

Description Logics (DLs) under Rational Closure (RC) is a well-known framework for non-monotonic reasoning in DLs. In this paper, we address the concept subsumption decision problem under RC for nominal safe ELO⊥, a notable and practically important DL representative of the OWL 2 profile OWL 2 EL. Our contribution here is to define a polynomial time subsumption procedure for nominal safe ELO⊥ under RC that relies entirely on a series of classical, monotonic EL⊥ subsumption tests. Therefore, any existing classical monotonic EL⊥ reasoner can be used as a black box to implement our method. We then also adapt the method to one of the known extensions of RC for DLs, namely Defeasible Inheritance-based DLs without losing the computational tractability

A polynomial Time Subsumption Algorithm for Nominal Safe ELO under Rational Closure

Description Logics (DLs) under Rational Closure (RC) is a well-known framework for non-monotonic reasoning in DLs. In this paper, we address the concept subsumption decision problem under RC for nominal safe ELO⊥, a notable and practically important DL representative of the OWL 2 profile OWL 2 EL. Our contribution here is to define a polynomial time subsumption procedure for nominal safe ELO⊥ under RC that relies entirely on a series of classical, monotonic EL⊥ subsumption tests. Therefore, any existing classical monotonic EL⊥ reasoner can be used as a black box to implement our method. We then also adapt the method to one of the known extensions of RC for DLs, namely Defeasible Inheritance-based DLs without losing the computational tractability

A polynomial Time Subsumption Algorithm for Nominal Safe ELO_bot under Rational Closure

Description Logics (DLs) under Rational Closure (RC) is a well-known framework for non-monotonic reasoning in DLs. In this paper, we address the concept subsumption decision problem under RC for nominal safe ELO_bot, a notable and practically important DL representative of the OWL 2 profile OWL 2 EL. Our contribution here is to define a polynomial time subsumption procedure for nominal safe ELO_bot under RC that relies entirely on a series of classical, monotonic EL_bot subsumption tests. Therefore, any existing classical monotonic EL_bot reasoner can be used as a black box to implement our method. We then also adapt the method to one of the known extensions of RC for DLs, namely Defeasible Inheritance-based DLs without losing the computational tractability

Principles of KLM-style Defeasible Description Logics

The past 25 years have seen many attempts to introduce defeasible-reasoning capabilities into a description logic setting. Many, if not most, of these attempts are based on preferential extensions of description logics, with a significant number of these, in turn, following the so-called KLM approach to defeasible reasoning initially advocated for propositional logic by Kraus, Lehmann, and Magidor. Each of these attempts has its own aim of investigating particular constructions and variants of the (KLM-style) preferential approach. Here our aim is to provide a comprehensive study of the formal foundations of preferential defeasible reasoning for description logics in the KLM tradition. We start by investigating a notion of defeasible subsumption in the spirit of defeasible conditionals as studied by Kraus, Lehmann, and Magidor in the propositional case. In particular, we consider a natural and intuitive semantics for defeasible subsumption, and we investigate KLM-style syntactic properties for both preferen- tial and rational subsumption. Our contribution includes two representation results linking our semantic constructions to the set of preferential and rational properties considered. Besides showing that our seman- tics is appropriate, these results pave the way for more effective decision procedures for defeasible reasoning in description logics. Indeed, we also analyse the problem of non-monotonic reasoning in description logics at the level of entailment and present an algorithm for the computation of rational closure of a defeasible knowledge base. Importantly, our algorithm relies completely on classical entailment and shows that the computational complexity of reasoning over defeasible knowledge bases is no worse than that of reasoning in the underlying classical DL ALC

Semantic Foundation for Preferential Description Logics

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