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We present a new approach for checking the compatibility of policy descriptions. At present, policies are widely used for explicitly expressing non-functional properties, capabilities, constraints and requirements of Web services. Policies are crucial in the negotiation phase of service discovery and selection. Typically, a potential service consumer has its own policy that specifies the conditions the service has to fulfill. Ideally, an automatic negotiation process identifies a mutually agreeable policy for both the Web service consumer and provider. WS-Policy defines policy intersection as a "first approximation" for determining the compatibility of policies. However, policy intersection has a major weakness: It is a purely syntactic approach neglecting the semantics of the involved policy assertions. In addition, it is unspecific on how to include domain-specific processing. In this paper we present a new solution that overcomes these deficits by introducing an entailment relation that reflects the semantics of assertions and policies. This paper not only discusses the formal foundations but also introduces the required algorithms such as "semantic policy differencing".