Declarative Semantics for P2P Data Management System

Abstract

The paper presents a logic-based framework for modeling the interaction among peers. It is assumed that each peer consists of a database, a set of standard logic rules, a set of mapping rules allowing to import a maximal set of atoms not leading to inconsistency and a set of integrity constraints. The proposal relies on previous works in Calvanese et al. (in: PODS, 2004) and Caroprese et al. (in: FLAIRS, 2006) where a (declarative) semantics for P2P systems is defined. Under this semantics, only facts not making the local databases inconsistent can be imported—Weak Models. This mechanism leads to the concept of Maximal Weak Models that are weak models in which peers import maximal sets of facts not violating integrity constraints. Different extensions to the basic framework, that aim at introducing significant mechanisms of preferences among different scenarios in the case of conflicting information, can be provided. This paper presents the basic framework of Maximal Weak Models and two extensions: the Trusted Weak Model Semantics and the Dynamic Weak Model Semantics. The Trusted Weak Model Semantics stems from the observation that the framework proposed in Calvanese et al. (in: PODS, 2004) and Caroprese et al. (in: FLAIRS, 2006) does not provide any mechanism to set priorities among mapping rules, rules that “integrate” data of a source peer into the database of a target peer. Anyhow, while collecting data, it is quite natural for a source peer to associate different degrees of reliability to the portion of data provided by its neighbor peers. Therefore, this paper enhances the basic semantics by using priority levels among mapping rules in order to select the weak models containing a maximum number of mapping atoms according to their importance. We will call these weak models, Trusted Weak Models, and we will show they can be computed as stable models of a logic program with weak constraints. The Dynamic Weak Model Semantics further enhances the basic framework by introducing aggregates and different levels of preference criteria that are not rigid, i.e., fixed a priori at design time, but depends on the database instance. The extended framework allows to model concepts like “in the case of conflicting information, it is preferable to import data from the neighbor peer that can provide the maximum number of tuples” or “in the case of conflicting information, it is preferable to import data from the neighbor peer such that the sum of the values of an attribute is minimum” without selecting a priori preferred peers. We will call these weak models, Dynamic Weak Models, and we will show they can be computed as stable models of a logic program with a list of sets of priorities.