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Lifted Variable Elimination for Probabilistic Logic Programming

Published online by Cambridge University Press:  21 July 2014

ELENA BELLODI ,
EVELINA LAMMA ,
FABRIZIO RIGUZZI ,
VITOR SANTOS COSTA  and
RICCARDO ZESE
ELENA BELLODI
Affiliation:
Dipartimento di Ingegneria - Università di FerraraVia Saragat 1, 44122, Ferrara, Italy
EVELINA LAMMA
Affiliation:
Dipartimento di Ingegneria - Università di FerraraVia Saragat 1, 44122, Ferrara, Italy
FABRIZIO RIGUZZI
Affiliation:
Dipartimento di Matematica e Informatica - Università di FerraraVia Saragat 1, 44122, Ferrara, Italy
VITOR SANTOS COSTA
Affiliation:
CRACS/INESC-TEC and DCC-FCUP - Universidade do Porto, Rua do Campo Alegre, 1021/1055, 4169-007 Porto, Portugal (e-mail: name.surname@unife.it, vsc@dcc.fc.up.pt)
RICCARDO ZESE
Affiliation:
Dipartimento di Ingegneria - Università di FerraraVia Saragat 1, 44122, Ferrara, Italy
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Abstract

Lifted inference has been proposed for various probabilistic logical frameworks in order to compute the probability of queries in a time that depends on the size of the domains of the random variables rather than the number of instances. Even if various authors have underlined its importance for probabilistic logic programming (PLP), lifted inference has been applied up to now only to relational languages outside of logic programming. In this paper we adapt Generalized Counting First Order Variable Elimination (GC-FOVE) to the problem of computing the probability of queries to probabilistic logic programs under the distribution semantics. In particular, we extend the Prolog Factor Language (PFL) to include two new types of factors that are needed for representing ProbLog programs. These factors take into account the existing causal independence relationships among random variables and are managed by the extension to variable elimination proposed by Zhang and Poole for dealing with convergent variables and heterogeneous factors. Two new operators are added to GC-FOVE for treating heterogeneous factors. The resulting algorithm, called LP2 for Lifted Probabilistic Logic Programming, has been implemented by modifying the PFL implementation of GC-FOVE and tested on three benchmarks for lifted inference. A comparison with PITA and ProbLog2 shows the potential of the approach.

Keywords

Probabilistic Logic ProgrammingLifted InferenceVariable EliminationDistribution SemanticsProbLogStatistical Relational Artificial Intelligence
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. 681 - 695
Copyright
Copyright © Cambridge University Press 2014 

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