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This thesis studies the problem of determining the satisfiability of a Boolean combination of binary difference constraints of the form x-y where x and y are numeric variables and constant. In particular,we present y can incremental and model-based inter preter for the theory of difference constraints in the context of a generic Boolean satisfiability checking procedure capable of incorporating interpreters for arbitrary theories. We show how to use the model based approach to efficiently make inferences with the option of complete inference.