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This paper considers the design of negotiation protocols for logic-based agent communication languages.We begin by motivating the use of such languages, and introducing a formal model of logic-based negotiation. Using this model, we define two important computational problems: the success problem (given a particular negotiation history, has agreement been reached?) and the guaranteed success problem (does a particular negotiation protocol guarantee that agreement will be reached?) We then consider a series of progressively more complex negotiation languages, and consider the complexity of using these languages. We conclude with a discussion on related work and issues for the future.