Outlier detection in default logics: the tractability/intractability frontier
F. Angiulli, R. Ben-Eliyahu-Zohary, L. Palopoli

TL;DR
This paper explores the computational boundaries of detecting outliers in default logics, identifying tractable cases, and providing algorithms within specific logical fragments, thereby advancing understanding of complexity and expressive power.
Contribution
It characterizes the tractability frontier for outlier detection in default logics, introduces a polynomial algorithm for strong outliers, and demonstrates that simple logic fragments can express all NL queries.
Findings
Polynomial time algorithm for enumerating strong outliers
Identification of tractable cases in default logic fragments
Normal unary theories can express all NL queries
Abstract
In default theories, outliers denote sets of literals featuring unexpected properties. In previous papers, we have defined outliers in default logics and investigated their formal properties. Specifically, we have looked into the computational complexity of outlier detection problems and proved that while they are generally intractable, interesting tractable cases can be singled out. Following those results, we study here the tractability frontier in outlier detection problems, by analyzing it with respect to (i) the considered outlier detection problem, (ii) the reference default logic fragment, and (iii) the adopted notion of outlier. As for point (i), we shall consider three problems of increasing complexity, called Outlier-Witness Recognition, Outlier Recognition and Outlier Existence, respectively. As for point (ii), as we look for conditions under which outlier detection can be…
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Taxonomy
TopicsLogic, Reasoning, and Knowledge · Formal Methods in Verification · Advanced Algebra and Logic
