Application of Possibilistic Stable Models to Decision Making

This paper investigates the applicability of Possibilistic Stable Models (PSM) for Logic Programming to decision making through the use of several extensions to the PSM formalism that are chosen to enhance the realism in the resulting decision making model. The selected extensions to PSMs are unified through their incorporation into an argumentation framework designed to represent the combined formalism. A PSM for a logic program is initially mapped to a Possibilistic preferred extension of the argumentation framework. This is first used as the basis for a particular type of strength comparison between arguments where the rule weights are interpreted as utilities. The framework is then extended to a value-based system incorporating context dependent utilities, and uncertainty in its domain knowledge. The strengths of arguments are assessed using an aggregation function combining all the significant magnitude information present in the argument. The concept of value projection rules are introduced that serve to provide domain context sensitivity for the mapping of circumstances onto values. Together with the aggregation function, this constitutes a method for realizing dynamic decision framing: the determination of the basis or grounds for the decision. An example of some realism is identified from Psychology literature based on an ethical dilemma familiar to contemporary moral philosophers. This example is presented to the system using a standard axiomatization for knowledge representation. Through the choice of a very general aggregation function, the dilemma exemplifies how the defined system capabilities may act together to realize a meaningful decision function, which is later independently characterized.