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Web and peer-to-peer systems have emerged as popular areas in distributed computing, and their integrated usage permits the benefits of both to be exploited. While much work in these areas have utilized the imperative programming paradigm, the need for declarative programming paradigms is increasingly being recognized, not only for the often cited advantages such as a higher level of abstraction and specialized language features, but also to tackle the querying and manipulation of knowledge and reasoning with semantics that will be the mainstay of the proposed next generation of the Web and peer-to-peer computing. This paper presents an approach towards integrative use of the Web and peer-to-peer systems within a declarative programming paradigm. We contend that logic programming can be useful in peer-to-peer computing, especially for querying and representing knowledge shared over peer networks, and for scripting applications that involve sophisticated search behaviour over peer networks. As an example of peer-to-peer querying expressed in a logic programming language, we propose a simple extension of Prolog, which we call LogicPeer, to enable goal evaluation over peers in a peer network. Using LogicPeer, we outline how a peer-to-peer version of a Yahoo-like system can be built and queried, and several other applications that involve decentralized knowledge sharing. We then show how LogicPeer can be used with LogicWeb, a Prolog extension to access Web pages, thereby integrating peer-to-peer querying and Web querying in a common declarative framework.