In traditional logic, an enthymeme is said to be an argument, or chain of argumentation, with one or more missing (implicit) premises or conclusions. In this paper a new theory of enthymemes, based on recent developments in argumentation technology including argumentation schemes, argument visualization tools and formal dialogue systems, is put forward. The dialogical theory hypothesizes three bases for the enthymeme in a formal dialogue system CBVK: (1) the participants' commitment sets, (2) sets of argumentation schemes (especially including presumptive schemes) shared by both participants, and (3) a set of propositions representing common knowledge shared by both participants. The formal dialogue system CBVK is the backbone of the theory of enthymemes into which these three components are built. Three examples of enthymemes of a kind commonly found in everyday conversational argumentation are used to show how the theory applies. © 2007 Elsevier B.V. All rights reserved.
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