A Logic of Argumentation for Reasoning Under Uncertainty

Abstract

We present the syntax and proof theory of a logic of argumentation, LA. We also outline the development of a category theoretic semantics for LA. L A is the core of a proof theoretic model for reasoning under uncertainty. In this logic, propositions are labeled with a representation of the arguments which support their validity. Arguments may then be aggregated to collect more information about the potential validity of the propositions of interest. We make the notion of aggregation primitive to the logic, and then define strength mappings from sets of arguments to one of a number of possible dictionaries. This provides a uniform framework which incorporates a number of numerical and symbolic techniques for assigning subjective confidences to propositions on the basis of their supporting arguments. These aggregation techniques are also described with examples.

Agents that reason and negotiate by arguing

“…The pair (<p, G) may also be extended to the triple (<p, G, a) to take account of the fact that <p may not be known to be true by giving it a degree of belief a [22]. The remainder of this section extends this system of argumentation to the multiagent case and demonstrates how it can be used within the agent architecture introduced in Section 3.…”

“…The system of argumentation which we use as the basis for negotiation is based upon that proposed by Fox and colleagues [11,22]. As with many systems of argumentation, it works by constructing series of logical steps (arguments) for and against propositions of interest and as such may be seen as an extension of classical logic.…”

Towards a Formal Account of Reasoning about Evidence: Argumentation Schemes and Generalisations

“…By contrast, in formalisms that somehow aggregate multiple reasons, such as Bayesian Networks, Reason-based logic (Hage, 1996) or Krause et al's (1995) LA system it suffices to represent a link from each individual observation statement to the supported claim; the aggregation mechanism ensures that only the applicable statements exert their influence on the claim (note, however, that in such formalism the strength of the combined reasons is still independent of the strengths of the individual reasons; this agrees with Pollock's analysis of accrual). It remains to be seen whether this difference is an advantage or a disadvantage of the present approach.…”

An appreciation of John Pollock's work on the computational study of argument

“…4. Although some terminological confusion has arisen since others (Krause, Ambler, Elvang-Gøransson, and Fox 1995, Besnard and Hunter 2001, Amgoud and Cayrol 2002 have used it for attack on a premise instead of on the application of a defeasible inference rule. 5.…”