A logic based approach for managing incompleteness and inconsistencies in P2P deductive databases

This paper proposes a logic framework for modeling the interaction among incomplete and inconsistent deductive databases in a P2P environment. It stems from the work in [9, 13, 14, 16, 17] in which the declarative semantics of a P2P system is defined in terms of maximal weak models and the work in [15] in which the declarative semantics of a P2P system is defined in terms of minimal weak models. The maximal weak models semantics is based on the idea to use the mapping rules to import in each peer as much knowledge as possible without violating local integrity constraints. On the other hand under the Minimal Weak Models Semantics each peer uses its mapping rules to import minimal sets of mapping atoms allowing to satisfy its local integrity constraints. This latter behavior turns out to be useful in real world P2P systems in which peers often use the available import mechanisms to extract knowledge from the rest of the system only if this knowledge is strictly needed to repair an inconsistent local database. Therefore, each peer can be thought of as a resource used either to enrich (integrate) the knowledge (Maximal Weak Model Semantics) or to fix (repair) the knowledge (Minimal Weak Model Semantics). This paper extends previous works in [9, 13, 14, 16, 17] and in [15] by proposing a rewriting technique that allows modeling a P2P system, PS, as a unique logic program whose stable models correspond either to the maximal or minimal weak models of PS.