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In many situations it is necessary to make decisions that depend on the outcomes of several different classifiers in a way that provides a coherent inferences that satisfies some constraint. These constraints might arise from the sequential nature of the data or other domain specific constraints. We study several general approaches to this problem and are evaluating those in the context of inference problemsin natural language -- identifying phrase structure and question-answering. The approaches studied are: (1) A Markovian approach that extends standard HMMs to allow the use of a state-observation dependencies. We study both generative and conditional models. (2) Extensionsof constraint satisfaction formalisms. Currently the focus is on developing hierarchical models. (3) Markov Random fields. We study a more general model in which constraints of more general structures can be devloped.