Extending the Notion of Preferred Explanations for Quantified Constraint Satisfaction Problems
The Quantified Constraint Satisfaction Problem (QCSP) is a generalization of classical constraint satisfaction problem in which some variables can be universally quantified. This additional expressiveness can help model problems in which a subset of the variables take value assignments that are outside the control of the decision maker. Typical examples of such domains are game-playing, conformant planning and reasoning under uncertainty. In these domains decision makers need explanations when a QCSP does not admit a winning strategy. We extend our previous approach to defining preferences amongst the requirements of a QCSP by considering more general relaxation schemes. We also present key complexity results on the hardness of finding preferred conflicts of QCSPs under this extension of the notion of preference. This paper unifies work from the fields of constraint satisfaction, explanation generation, and reasoning under preferences and uncertainty.
KeywordsConsistency Check Total Order Relaxation Function Universal Quantifier Equivalent Class
This material is based upon work supported by the Science Foundation Ireland under Grant No.10/CE/I1853 and the FP7 Programme (FP7/2007–2013) under grant agreement No. 318137 (DISCUS). The Insight Centre for Data Analytics is also supported by Science Foundation Ireland under Grant No. SFI/12/RC/2289.
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