In peer-to-peer data integration, each peer exports data in terms of its own schema, and data interoperation is achieved by means of mappings among the peer schemas. Peers are autonomous systems and mappings are dynamically created and changed. One of the challenges in these systems is an-swering queries posed to one peer taking into account the mappings. Obviously, query answering strongly depends on the semantics of the overall system. In this paper, we com-pare the commonly adopted approach of interpreting peer-to-peer systems using a first-order semantics, with an al-ternative approach based on epistemic logic. We consider several central properties of peer-to-peer systems: modular-ity, generality, and decidability. We argue that the approach based on epistemic logic is superior with respect to all the above properties. In particular, we show that, in systems in which peers have decidable schemas and conjunctive map-pings, but are arbitrarily interconnected, the first-order ap-proach may lead to undecidability of query answering, while the epistemic approach always preserves decidability. This is a fundamental property, since the actual interconnections among peers are not under the control of any actor in the system.
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