On Complexity and Generality of Contrary Prioritized Defeasible Theory

This paper studies defeasible logic for representing legal theories. In defeasible logic, a literal can be ambiguous since a theory can support both the literal and its contrary. There have been several policies in handling ambiguities but choosing a policy is under judges’ discretion, which is unpredictable and possibly contradicts the legislators’ intentions. To prevent such a problem, this paper studies contrary prioritization, which restricts a defeasible theory to prioritize all pairs of rules in which heads are contrary to each other. This paper analyzes the complexity of contrary prioritization and the generality of contrary prioritized defeasible theories in the translations between such defeasible theories and stratified logic programs. This paper presents that contrary prioritization requires an effort of finding a correct assignment of the priorities between contrary pairs, and the effort makes the problem of contrary prioritization NP-complete. Furthermore, every contrary prioritized defeasible theory can be translated to a stratified logic program and vice versa. Hence, a contrary prioritized defeasible theory is as general as a stratified logic program.