Distributed Reasoning with Conflicts in a Multi-Context Framework

A Multi-Context System consists of a set of contexts and a set of inference rules (known as mapping or bridge rules) that enable information flow between different contexts. A context can be thought as a logical theory a set of axioms and inference rules that models local context knowledge. Different contexts are expected to use different languages and inference systems, and although each context may be locally consistent, global consistency cannot be required or guaranteed. Reasoning with multiple contexts requires performing two types of reasoning; (a) local reasoning, based on the individual context theories; and (b) distributed reasoning, which combines the consequences of local theories using the mappings. The most critical challenges of contextual reasoning are; (a) the heterogeneity of local context theories; and (b) the potential conflicts that may arise from the interaction of different contexts through the mappings. Our study mainly focuses on the second issue, by modeling the different contexts as peers in a P2P system, and performing some type of defeasible reasoning on the distributed peer theories. Two recent studies that deploy non-monotonic reasoning approaches in Multi-Context Systems are the nonmonotonic rule-based MCS framework, which supports default negation in the mapping rules, proposed in (Roelofsen and Serafini 2005), and the multi-context variant of Default Logic presented in (Brewka, Roelofsen, and Serafini 2007). The latter models the bridge relations between different contexts as default rules, and has the additional advantage that is closer to implementation due to the well-studied relation between Default Logic and Logic Programming. However, the authors do not provide specific reasoning algorithms e.g. for query evaluation, leaving some practical issues, such as the integration of priority information, unanswered. Our study also relates to several studies that are focused on the semantic characterization of mappings in peer data management systems. Among them, (Franconi et al. 2003), (Calvanese et al. 2005), and (Chatalic, Nguyen, and Rousset 2006) are the most prominent that deal with inconsistencies. The first one is based on auto-epistemic semantics and handles only local inconsistency. The second is based on non-