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The P-Box CDF-Intervals: A Reliable Constraint Reasoning with Quantifiable Information

Published online by Cambridge University Press:  21 July 2014

AYA SAAD ,
THOM FRÜHWIRTH  and
CARMEN GERVET
AYA SAAD
Affiliation:
Universität Ulm, Germany (e-mail: ayas@aucegypt.edu, thom.fruehwirth@uni-ulm.de)
THOM FRÜHWIRTH
Affiliation:
Universität Ulm, Germany (e-mail: ayas@aucegypt.edu, thom.fruehwirth@uni-ulm.de)
CARMEN GERVET
Affiliation:
Université de Savoie, France (e-mail: gervetec@univ-savoie.fr)
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Abstract

This paper introduces a new constraint domain for reasoning about data with uncertainty. It extends convex modeling with the notion of p-box to gain additional quantifiable information on the data whereabouts. Unlike existing approaches, the p-box envelops an unknown probability instead of approximating its representation. The p-box bounds are uniform cumulative distribution functions (cdf) in order to employ linear computations in the probabilistic domain. The reasoning by means of p-box cdf-intervals is an interval computation which is exerted on the real domain then it is projected onto the cdf domain. This operation conveys additional knowledge represented by the obtained probabilistic bounds. The empirical evaluation of our implementation shows that, with minimal overhead, the output solution set realizes a full enclosure of the data along with tighter bounds on its probabilistic distributions.

Keywords

convex structuresreliable constraint reasoningprobability boxcdf intervalconstraint satisfaction problemconstraint programmingconstraint reasoninguncertainty
Type
Regular Papers
Information
Theory and Practice of Logic Programming , Volume 14 , Special Issue 4-5: 30th International Conference on Logic Programming , July 2014 , pp. 461 - 475
Copyright
Copyright © Cambridge University Press 2014 

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