Complexity of Prioritized Default Logics

TL;DR

This paper analyzes the computational complexity of three formalizations of prioritized default logic, comparing their placement within the polynomial hierarchy and identifying tractable subclasses.

Contribution

It provides a detailed complexity analysis of three prioritized default logics within Reiter's framework, highlighting their computational boundaries.

Findings

Propositional variants are on the second and third levels of the polynomial hierarchy.

Identifies boundaries between tractable and intractable inference.

Compares three formalizations: Baader and Hollunder, Brewka, and lexicographic-based logic.

Abstract

In default reasoning, usually not all possible ways of resolving conflicts between default rules are acceptable. Criteria expressing acceptable ways of resolving the conflicts may be hardwired in the inference mechanism, for example specificity in inheritance reasoning can be handled this way, or they may be given abstractly as an ordering on the default rules. In this article we investigate formalizations of the latter approach in Reiter's default logic. Our goal is to analyze and compare the computational properties of three such formalizations in terms of their computational complexity: the prioritized default logics of Baader and Hollunder, and Brewka, and a prioritized default logic that is based on lexicographic comparison. The analysis locates the propositional variants of these logics on the second and third levels of the polynomial hierarchy, and identifies the boundary between tractable and intractable inference for restricted classes of prioritized default theories.