# Polite Theories Revisited

Polite Theories Revisited” by Dejan Jovanovic and Clark Barrett. In Proceedings of the 17^th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning (LPAR '10), (Christian G. Fermüller and Andrei Voronkov, eds.), Oct. 2010, pp. 402-416. Yogyakarta, Indonesia.

## Abstract

The classic method of Nelson and Oppen for combining decision procedures requires the theories to be stably-infinite. Unfortunately, some important theories do not fall into this category (e.g. the theory of bit-vectors). To remedy this problem, previous work introduced the notion of polite theories. Polite theories can be combined with any other theory using an extension of the Nelson-Oppen approach. In this paper we revisit the notion of polite theories, fixing a subtle flaw in the original definition. We give a new combination theorem which specifies the degree to which politeness is preserved when combining polite theories. We also give conditions under which politeness is preserved when instantiating theories by identifying two sorts. These results lead to a more general variant of the theorem for combining multiple polite theories.

BibTeX entry:

@inproceedings{JB10-LPAR,
author = {Dejan Jovanovi{\'c} and Clark Barrett},
editor = {Christian G. Ferm{\"u}ller and Andrei Voronkov},
title = {Polite Theories Revisited},
booktitle = {Proceedings of the {\it 17^{th}} International Conference
on Logic for Programming, Artificial Intelligence, and Reasoning
(LPAR '10)},
series = {Lecture Notes in Computer Science},
volume = {6397},
pages = {402--416},
publisher = {Springer},
month = oct,
year = {2010},
isbn = {3-642-16241-X, 978-3-642-16241-1},
issn = {0302-9743},
note = {Yogyakarta, Indonesia},
url = {http://www.cs.nyu.edu/~barrett/pubs/JB10-LPAR.pdf}
}


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