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We describe a probabilistic approach for the interpretation of user arguments that integrates three aspects of an interpretation: inferences, suppositions and explanatory extensions. Inferences fill in information that connects the propositions in a user’s argument, suppositions postulate new information that is likely believed by the user and is necessary to make sense of his or her argument, and explanatory extensions postulate information the user may have implicitly considered when constructing his or her argument. Our system receives as input an argument entered through a web interface, and produces an interpretation in terms of its underlying knowledge representation—a Bayesian network. Our evaluations show that suppositions and explanatory extensions are necessary components of interpretations, and that users consider appropriate the suppositions and explanatory extensions postulated by our system. [ABSTRACT FROM AUTHOR]