Strong Backdoors for Default Logic

Abstract

In this paper, we introduce a notion of backdoors to Reiter’s propositional default logic and study structural properties of it. Also we consider the problems of backdoor detection (parameterised by the solution size) as well as backdoor evaluation (parameterised by the size of the given backdoor), for various kinds of target classes (CNF, KROM, MONOTONE) and all SCHAEFER classes. Also, we study generalisations of HORN-formulas, namely, QHORN, RHORN, as well as DUALHORN. For these classes, we also classify the computational complexity of the implication problem. We show that backdoor detection is fixed-parameter tractable for the considered target classes, and prove a complete trichotomy for backdoor evaluation. The problems are either fixed-parameter tractable, para-DeltaP2-complete, or para-NP-complete, depending on the target class.