Katarina Britz

Semantic foundation for preferential description logics

Description logics are a well-established family of knowledge representation formalisms in Artificial Intelligence. Enriching description logics with non-monotonic reasoning capabilities, especially preferential reasoning as developed by Lehmann and colleagues in the 90s, would therefore constitute a natural extension of such KR formalisms. Nevertheless, there is at present no generally accepted semantics, with corresponding syntactic characterization, for preferential consequence in description logics. In this paper we fill this gap by providing a natural and intuitive semantics for defeasible subsumption in the description logic

Preferential Reasoning for Modal Logics

\mathcal{ALC}

Introducing Role Defeasibility in Description Logics

. Our semantics replaces the propositional valuations used in the models of Lehmann et al.. with structures we refer to as concept models . We present representation results for the description logic

ABox abduction in ALC using a DL tableau

\mathcal{ALC}

From KLM-style conditionals to defeasible modalities, and back

for both preferential and rational consequence relations. We argue that our semantics paves the way for extending preferential and rational consequence, and therefore also rational closure, to a whole class of logics that have a semantics defined in terms of first-order relational structures.

Preferential Accessibility and Preferred Worlds

Modal logic is the foundation for a versatile and well-established class of knowledge representation formalisms in artificial intelligence. Enriching modal logics with non-monotonic reasoning capabilities such as preferential reasoning as developed by Lehmann and colleagues would therefore constitute a natural extension of such KR formalisms. Nevertheless, there is at present no generally accepted semantics, with corresponding syntactic characterization, for preferential consequence in modal logics. In this paper we fill this gap by providing a natural and intuitive semantics for preferential and rational modal consequence. We prove representation results for both preferential and rational consequence, which paves the way for effective decision procedures for modal preferential reasoning. We then illustrate applications of our constructions to modal logics widely used in AI, notably in the contexts of reasoning about actions, knowledge and beliefs. We argue that our semantics constitutes the foundation on which to explore preferential reasoning in modal logics in general.

Normal modal preferential consequence

Accounts of preferential reasoning in Description Logics often take as point of departure the semantic notion of a preference order on objects in a domain of interpretation, which allows for the development of notions of defeasible subsumption and entailment. However, such an approach does not account for defeasible roles, interpreted as partially ordered sets of tuples. We state the case for role defeasibility and introduce a corresponding preferential semantics for a number of defeasible constructs on roles. We show that this does not negatively affect decidability or complexity of reasoning for an important class of DLs, and that existing notions of preferential reasoning can be expressed in terms of defeasible roles.

Ontology Learning from Interpretations in Lightweight Description Logics

The formal definition of abduction asks what needs to be added to a knowledge base to enable an observation to be entailed by the knowledge base. ABox abduction in description logics (DLs) asks what ABox statements need to be added to a DL knowledge base to allow an observation (also in the form of ABox statements) to be entailed. Klarman et al have provided an algorithm for performing ABox abduction in the description logic ALC by converting the knowledge base and observation to first-order logic, using a connection tableau to obtain abductive solutions, and then converting these back to DL syntax. In this paper we describe how this can be done directly using a DL tableau.

Reachability Modules for the Description Logic \mathcal{SRIQ}

Abstract We investigate an aspect of defeasibility that has somewhat been overlooked by the non-monotonic reasoning community, namely that of defeasible modes of reasoning. These aim to formalise defeasibility of the traditional notion of necessity in modal logic, in particular of its different readings as action, knowledge and others in specific contexts, rather than defeasibility of conditional forms. Building on an extension of the preferential approach to modal logics, we introduce new modal osperators with which to formalise the notion of defeasible necessity and distinct possibility, and that can be used to represent expected effects, refutable knowledge, and so on. We show how KLM-style conditionals can smoothly be integrated with our richer language. We also propose a tableau calculus which is sound and complete with respect to our modal preferential semantics, and of which the computational complexity remains in the same class as that of the underlying classical modal logic.

Rationality and Context in Defeasible Subsumption

Modal accounts of normality in non-monotonic reasoning traditionally have an underlying semantics based on a notion of preference amongst worlds. In this paper, we motivate and investigate an alternative semantics, based on ordered accessibility relations in Kripke frames. The underlying intuition is that some world tuples may be seen as more normal, while others may be seen as more exceptional. We show that this delivers an elegant and intuitive semantic construction, which gives a new perspective on defeasible necessity. Technically, the revisited logic does not change the expressive power of our previously defined preferential modalities. This conclusion follows from an analysis of both semantic constructions via a generalisation of bisimulations to the preferential case. Reasoners based on the previous semantics therefore also suffice for reasoning over the new semantics. We complete the picture by investigating different notions of defeasible conditionals in modal logic that can also be captured within our framework.