Power Defaults

This paper introduces power default reasoning (PDR), a framework for nonmonotonic reasoning based on the domain-theoretic idea of modeling default rules with partial-information in a higher-order setting. PDR lifts a non-monotonic operator at the base (syntactic) level to a well-behaved, almost monotonic operator in the higher-order space of the Smyth power-domain – effectively a space of sets of models. Working in the model space allows us to prove the dichotomy theorem and the extension splitting theorem, leading to a more well-behaved logic and (modulo the usual complexity conjectures) a less complex logic than standard default logic. Specifically, we prove that skeptical normal default inference is a problem complete for co-NP(3) in the Boolean hierarchy for strict propositional logic and NP(4)-complete in general. These results (by changing the underlying semantics) contrasts favorably with similar results of Gottlob [9], who proves that standard skeptical default reasoning i...

• Type: Conference
• Year: 1997
• Where: LPNMR
• Authors: Guo-Qiang Zhang, William C. Rounds
• Keywords: Automated Reasoning, Default Logic, Default Reasoning, Extension Splitting Theorem, LPNMR 1997