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The magic of logical inference in probabilistic programming

Published online by Cambridge University Press:  06 July 2011

BERND GUTMANN ,
INGO THON ,
ANGELIKA KIMMIG ,
MAURICE BRUYNOOGHE  and
LUC DE RAEDT
BERND GUTMANN
Affiliation:
Department of Computer Science, Katholieke Universiteit Leuven, Celestijnenlaan 200A-bus 2402, 3001 Heverlee, Belgium (e-mail: bernd.gutmann@cs.kuleuven.be, ingo.thon@cs.kuleuven.be, angelika.kimmig@cs.kuleuven.be, maurice.bruynooghe@cs.kuleuven.be, luc.deraedt@cs.kuleuven.be)
INGO THON
Affiliation:
Department of Computer Science, Katholieke Universiteit Leuven, Celestijnenlaan 200A-bus 2402, 3001 Heverlee, Belgium (e-mail: bernd.gutmann@cs.kuleuven.be, ingo.thon@cs.kuleuven.be, angelika.kimmig@cs.kuleuven.be, maurice.bruynooghe@cs.kuleuven.be, luc.deraedt@cs.kuleuven.be)
ANGELIKA KIMMIG
Affiliation:
Department of Computer Science, Katholieke Universiteit Leuven, Celestijnenlaan 200A-bus 2402, 3001 Heverlee, Belgium (e-mail: bernd.gutmann@cs.kuleuven.be, ingo.thon@cs.kuleuven.be, angelika.kimmig@cs.kuleuven.be, maurice.bruynooghe@cs.kuleuven.be, luc.deraedt@cs.kuleuven.be)
MAURICE BRUYNOOGHE
Affiliation:
Department of Computer Science, Katholieke Universiteit Leuven, Celestijnenlaan 200A-bus 2402, 3001 Heverlee, Belgium (e-mail: bernd.gutmann@cs.kuleuven.be, ingo.thon@cs.kuleuven.be, angelika.kimmig@cs.kuleuven.be, maurice.bruynooghe@cs.kuleuven.be, luc.deraedt@cs.kuleuven.be)
LUC DE RAEDT
Affiliation:
Department of Computer Science, Katholieke Universiteit Leuven, Celestijnenlaan 200A-bus 2402, 3001 Heverlee, Belgium (e-mail: bernd.gutmann@cs.kuleuven.be, ingo.thon@cs.kuleuven.be, angelika.kimmig@cs.kuleuven.be, maurice.bruynooghe@cs.kuleuven.be, luc.deraedt@cs.kuleuven.be)
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Abstract

Today, there exist many different probabilistic programming languages as well as more inference mechanisms for these languages. Still, most logic programming-based languages use backward reasoning based on Selective Linear Definite resolution for inference. While these methods are typically computationally efficient, they often can neither handle infinite and/or continuous distributions nor evidence. To overcome these limitations, we introduce distributional clauses, a variation and extension of Sato's distribution semantics. We also contribute a novel approximate inference method that integrates forward reasoning with importance sampling, a well-known technique for probabilistic inference. In order to achieve efficiency, we integrate two logic programming techniques to direct forward sampling. Magic sets are used to focus on relevant parts of the program, while the integration of backward reasoning allows one to identify and avoid regions of the sample space that are inconsistent with the evidence.

Keywords

probabilistic logicforward reasoningsamplingcontinuous distributions
Type
Regular Papers
Information
Theory and Practice of Logic Programming , Volume 11 , Special Issue 4-5: 27th International Conference on Logic Programming , July 2011 , pp. 663 - 680
Copyright
Copyright © Cambridge University Press 2011

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