Formalizing nonmonotonic reasoning systems
Artificial Intelligence
On the classification and existence of structures in default logic
Fundamenta Informaticae
Hard problems for simple default logics
Artificial Intelligence - Special issue on knowledge representation
The complexity of logic-based abduction
Journal of the ACM (JACM)
Semantics and complexity of abduction from default theories
Artificial Intelligence
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Yet some more complexity results for default logic
Artificial Intelligence
System Z: a natural ordering of defaults with tractable applications to nonmonotonic reasoning
TARK '90 Proceedings of the 3rd conference on Theoretical aspects of reasoning about knowledge
Outlier detection by logic programming
ACM Transactions on Computational Logic (TOCL)
Outlier detection using default reasoning
Artificial Intelligence
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Default logic is used to describe regular behavior and normal properties. We suggest to exploit the framework of default logic for detecting outliers -- individuals who behave in an unexpected way or feature abnormal properties. The ability to locate outliers can help to maintain knowledge-base integrity and to single out irregular individuals. We first formally define the notion of an outlier and an outlier witness. We then show that finding outliers is quite complex. Indeed, we show that several versions of the outlier detection problem lie over the second level of the polynomial hierarchy. For example, the question of establishing if at least one outlier can be detected in a given propositional default theory is Σ3P-complete. Although outlier detection involves heavy computation, the queries involved can frequently be executed offline, thus somewhat alleviating the difficulty of the problem. In addition, we show that outlier detection can be done in polynomial time for both the class of acyclic normal unary defaults and the class of acyclic dual normal unary defaults.