A Modal Defeasible Reasoner of Deontic Logic for the Semantic Web

Introduction

Defeasible Logic, originally introduced by Nute (1994), is a non-monotonic formalism that deals with incomplete and conflicting information. Compared to other more mainstream non-monotonic approaches (Gottlob, 1992; Kautz & Selman, 1991; Soininen & Niemela, 1998), this approach offers enhanced representational capabilities and low computational complexity. Defeasible reasoning can represent facts, rules, priorities and conflicts among rules. Such conflicts usually emerge in the case of rules with exceptions, which are a natural representation for policies and business rules (e.g., Rissland & Skalak, 1991; Schild & Herzog, 1993). In these cases priority information is often used in resolving conflicts among rules.

Modal Logic (Blackburn, de Rijke, & Venema, 2001), on the other hand, is a system of formal logic that deals with modalities, namely, expressions that are associated with the notions of possibility and necessity. However, modal logic is not restricted to these concepts, but can assume a variety of interpretations, depending on meaning, context and various other factors. Thus, according to the different interpretations, there exist diverse categories of modal logics, like epistemic logic that deals with the certainty of sentences (Meyer, 2001), deontic logic, which deals with the notions of obligation and permission (Hilpinen, 2001), temporal logic, which deals with temporal notions (Venema, 2001) and doxastic logic that deals with reasoning about beliefs (Meyer, 2003).

Modal logics are usually deployed as extensions to classical propositional logic with intentional operators. However, classical propositional logic requires complete, consistent and reliable information, requirements that are rarely met in real-life scenarios, which are by default defeasible in nature. Additionally, reasoning about motivational notions like beliefs, intentions or obligations, displays a significant degree of defeasibility. Consequently, instead of extending propositional logic, it is more appropriate to extend defeasible logic with modal logic elements and recent work confirms this trend (Governatori & Rotolo, 2004; Governatori, Hulstijn, Riveret, & Rotolo, 2007; Riveret, Rotolo, & Governatori, 2007).

The above types of logics are extremely suitable in the Semantic Web, which aims at enriching the available information on the Web with meaning, leading to better cooperation between end-users and applications (Berners-Lee, Hendler & Lassila, 2001). Defeasible and modal logics, in general, and deontic logic, in particular, can assist towards this direction, by providing means for modeling multi-agent systems (MAS), where each agent is characterized by its own cognitive profile and normative system, as well as policies, which define privacy requirements for a user, access permissions for a resource, individual rights, etc. Already, defeasible logic is applied in a number of related fields, like semantic brokering (Antoniou, Skylogiannis, Bikakis, & Bassiliades, 2007), security policies (Ashri, Payne, Marvin, Surridge, & Taylor, 2004), e-contracting (Governatori, 2005) and agent negotiations (Skylogiannis, Antoniou, Bassiliades, Governatori, & Bikakis, 2007) and, as the article argues, extending defeasible logic with deontic logic operators significantly improves our ability to model applications, naturally using concepts and notions similar to those we find in applications.