Nonmonotonicity and Partiality in Defeasible Argumentation

This chapter is concerned with nonmonotonicity and partiality in the theory of defeasible argumentation. In this theory, a defeasible proof (or argument) establishes warrant for a conclusion only if it is not defeated by better counterarguments. We introduce a formal theory of argumentation, in which the notion of abstract argumentation system is paramount. After that, we discuss the significance of studying general properties of warrant, and argue why most of these properties, notably cumulativity, fail to hold for even the most straightforward patterns of nonmonotonic reasoning. We even go as far as to claim that nonmonotonic entailment is characterised by nothing but nonmonotonicity. A theory of warrant declares which argument is in force and which is not, and might therefore be considered to comprise a declarative semantics. Even an ardent proponent of procedural argumentation would have little trouble with this statement. In addition, however, we state that a theory of warrant also comprises a model theoretic semantics. Knowing that some followers of the procedural school have balked at this, we support our claim by proving our version of warrant equivalent to a model theoretic partial semantics. We conclude by telling what procedural argumentation is supposed to be.

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