Reasoning with Preference Trees over Combinatorial Domains. Liu, X. & Truszczynski, M. In *Proceedings of the 4th International Conference on Algorithmic Decision Theory (ADT)*, volume 9346, pages 19-34, 2015. Springer (Acceptance rate: <font color="red">42%</font>). Paper abstract bibtex 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 define 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 key reasoning tasks of comparing outcomes with respect to orders defined by p-trees, and of finding optimal outcomes.

@inproceedings{conf/adt15/liuT,
author = {Xudong Liu and Miroslaw Truszczynski},
booktitle = {Proceedings of the 4th International Conference on Algorithmic Decision Theory (ADT)},
publisher = {Springer (Acceptance rate: <font color="red">42%</font>)},
%publisher = {Springer},
title = {Reasoning with Preference Trees over Combinatorial Domains},
url_Paper = {http://xudongliu.domains.unf.edu/resources/ptrees_adt15.pdf},
isbn = {978-3-319-23113-6},
pages = {19-34},
volume = 9346,
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
define 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 key reasoning tasks of comparing outcomes with respect to
orders defined by p-trees, and of finding optimal outcomes.},
year = 2015
}

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