Strong Backdoors for Default Logic

TL;DR

This paper introduces the concept of backdoors in propositional default logic, analyzing their structural properties, detection, and evaluation complexities across various target classes, with fixed-parameter tractability results.

Contribution

It defines backdoors for default logic, studies their structural properties, and establishes complexity results for detection and evaluation across multiple target classes.

Findings

Backdoor detection is fixed-parameter tractable for several classes.

Backdoor evaluation complexity varies by class, being either fixed-parameter tractable or in para-NP.

The study provides a framework for understanding the computational complexity of backdoors in 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, horn, krom, monotone, identity). We show that backdoor detection is fixed-parameter tractable for the considered target classes, and backdoor evaluation is either fixed-parameter tractable, in para-DP2 , or in para-NP, depending on the target class.