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Declarative Semantics for P2P Data Management System

  • Original Article
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Journal on Data Semantics

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.

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Notes

  1. The special syntax used for a fact—its first part is the peer identifier—will be formally presented in Sect. 3.

  2. The precise syntax and semantics of mapping rules will be formally defined in Sect. 3.

  3. We use for the operator and both ‘, ’ and ‘\(\wedge \).’

  4. Higher values for priority levels mark weak constraints of higher importance.

  5. A program with a weak constraint \(\Leftarrow p(X)\) can be regarded as modeling a minimization problem whose objective function is the cardinality of p.

  6. Whenever the reference to a peer predicate (resp. peer atom, peer literal, peer fact, peer rule, peer standard rule, peer integrity constraint, peer mapping rule ) is clear from the context, the term peer can be omitted.

  7. A built-in atom is of the form \(\theta (X,Y)\), where X and Y are terms and \(\theta \in \{<,>,\le ,\ge ,=,\ne \}\). It is also denoted as \(X\ \theta \ Y\).

  8. In fact, under stable model semantics a strong constraint of the form \(\leftarrow {\mathscr {B}}\) is actually a shorthand for \(p \leftarrow {\mathscr {B}}, \lnot p\).

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Authors and Affiliations

  1. ICAR-CNR, Quattromiglia, Italy

    Luciano Caroprese

  2. DIMES, Università della Calabria, Via Pietro Bucci, 87036, Rende, Italy

    Ester Zumpano

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  1. Luciano Caroprese
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  2. Ester Zumpano
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Correspondence to Ester Zumpano.

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Caroprese, L., Zumpano, E. Declarative Semantics for P2P Data Management System. J Data Semant 9, 101–122 (2020). https://doi.org/10.1007/s13740-020-00115-6

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