Logic of Probabilistic Arguments

1 CHARLES RIVER ANALYTICS, Cambridge, MA 02138, USA Abstract We present a logic for reasoning with probabilistic arguments to help decision making under uncertainty. The syntax of the logic is essentially modal propositional, and arguments of decision makers are expressed as sentences of the logic, with associated supports drawn from a probability dictionary. To aggregate a set of arguments for and against some decision options, we construct a Bayesian belief network based on the argument set without requiring any additional information from the decision-maker. Evidence converted from the underlying knowledge of the decision maker is posted at the relevant nodes of the belief network to compute probability distributions, and hence rankings, among the decision options. Decision-making based on such rankings of decision options is therefore guaranteed to be consistent with probability theory. We develop possible world semantics of the logic, and establish soundness and completeness results. We illustrate the proposed decision-making framework in the context of a concrete example.