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In order to facilitate the mapping between the WSML variant and the underlying logic, the WSML ontology is rst transformed to a set of normalized logical expressions, according to Table 101 Then, this normalized set of logical expressions is mapped to the logic using the mapping function p Finally, satis ability and entailment are de ned wrt this transformed WSML ontology The semantics of WSML is de ned through a mapping to a wellknown formalism rather than giving a direct semantics, in order to facilitate understanding of the language and so that complexity results follow immediately from the de nitions and the known literature.

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[1] T.C. Chiueh, C. Venkatramani, and M. Vernick, Design and Implementation of the Stony Brook Video Server, Technical Report TR-16, Computer Science Department, State University of New York at Stony Brook, August 1995. [2] F.A. Tobagi and J. Pang, StarWorks: A Video Applications Server, IEEE COMPCON Spring 93, 1993, pp. 4 11. [3] R. Buck, The Oracle Media Server for nCube Massively Parallel Systems, Proceedings of 8th International Parallel Processing Symposium, 1994, pp. 670 673. [4] H. Taylor, D. Chin, and S. Knight, The Magic Video-on-Demand Server and Real-Time Simulation System, IEEE Parallel and Distributed Technology: Systems and Applications, vol. 3, no. 2, 1995, pp. 40 51. [5] D.J. Gemmell, H.M. Vin, D.D. Kandlur, P.V. Rangan, and L.A. Rowe, Multimedia Storage Servers: A Tutorial, IEEE Computer, vol. 28, no. 5, May 1995, pp. 40 49. [6] D. Mills, Internet Time Synchronization: The Network Time Protocol, IEEE Transactions on Comm., vol. 39, no. 10, Oct. 1991, pp. 1482 1493. [7] Z. Yang and T.A. Marsland, (eds) Global States and Time in Distributed Systems, IEEE Computer Society Press, Los Alamitos, CA, USA, 1994. [8] P.S. Yu, M.S. Chen, and D.D. Kandlur, Grouped Sweeping Scheduling for DASD-based Multimedia Storage Management, ACM Multimedia Systems, vol. 1, 1993, pp. 99 109. [9] J.N. Lloyd and K.S. Samuel, Urn Models and their Application, John Wiley & Sons, 1997, pp. 125 126.

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One potential problem with the concurrent-push architecture, and any parallel server architectures in general, is reliability. As the system distributes video data over multiple servers, failure of a single server will cripple the entire system. Worst still, as the system is scaled up to more users, more servers will be needed and consequently the system-wide reliability will decrease accordingly. Drawing similar principles from disk array researches, we present in this chapter fault-tolerant algorithms to improve the system reliability. In particular, we address three key problems pertaining to supporting fault tolerance in the concurrent-push architecture, namely, redundancy management, redundant data transmission protocol, and real-time fault masking. First, redundant data based on erasure codes are introduced to video data stored in the servers, which are then delivered to the clients to support fault tolerance. Despite the success of distributed redundancy striping schemes such as RAID-5 in disk array implementations, we discover that similar schemes extended to the server context do not scale well. Instead, we develop a redundant server scheme that is both scalable and consumes less server buffer. Second, two protocols are introduced to control the transmission of redundant data to the clients, namely, forward erasure correction (FEC) and progressive redundancy transmission (PRT). These two protocols achieve different tradeoffs between bandwidth overhead, implementation complexity, and client buffer requirement. Finally, we derive the amount of client buffers required so that non-stop, continuous video playback can be maintained during server failure.

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In order to give an idea of the semantics, we show the example ontology amazonBooks transformed to F-Logic Programming: x y ) z ^ w y ! v ^ not v : z ) ! amazon Book title ) string ) cart id ) string ) x : cart ^ not x id ! y ! x : cart ^ x id ! y ^ x id ! z ^ y 6 z ! ! cart items ) amazon Book ) Note that in the example, a rule without a head is an integrity constraint A model of the rule base violates an integrity constraint if the body of the constraint is true in the model We call a transformed WSML-Flight ontology O satis able iff the transformed rule base p(O) (without the constraints) has a perfect model MO (Kifer et al.

To support server-level fault tolerance, we need redundant data so that a client can re-compute the unavailable video data after server failures. The problem of correcting data errors has been studied extensively in the literature. According to coding theory [1], one can encode a set of symbols with redundancies so that errors occurring within the set can be corrected later. However, server failure is slightly different in the sense that there is really no error in the coding sense. Instead, a server failure introduces erasures the absence of data.

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