Abstract
Preference trees, or P-trees for short, offer an intuitive and often concise way of representing preferences over combinatorial domains. In this paper, we propose an alternative definition of P-trees, and formally introduce their compact representation that exploits occurrences of identical subtrees. We show that P-trees generalize lexicographic preference trees and are strictly more expressive. We relate P-trees to answer-set optimization programs and possibilistic logic theories. Finally, we study reasoning with P-trees and establish computational complexity results for the key reasoning tasks of comparing outcomes with respect to orders defined by P-trees, and of finding optimal outcomes.
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Notes
- 1.
We overload the symbols \(\succeq _T\) and \(\succ _T\) by using them both for the order on the leaves of T and the corresponding preorder on the outcomes from \( CD (\mathcal {I})\).
- 2.
This definition is a slight adaptation of the original one.
- 3.
Given a Boolean formula \(\varPhi \) over \(\{x_1,\ldots ,x_n\}\), the maximum satisfying assignment (MSA) problem is to decide whether \(x_n=1\) in the lexicographically maximum satisfying assignment for \(\varPhi \). (If \(\varPhi \) is unsatisfiable, the answer is \(\textit{no}\).).
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Liu, X., Truszczynski, M. (2015). Reasoning with Preference Trees over Combinatorial Domains. In: Walsh, T. (eds) Algorithmic Decision Theory. ADT 2015. Lecture Notes in Computer Science(), vol 9346. Springer, Cham. https://doi.org/10.1007/978-3-319-23114-3_2
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DOI: https://doi.org/10.1007/978-3-319-23114-3_2
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