TY - JOUR
T1 - The PITA system
T2 - Tabling and answer subsumption for reasoning under uncertainty
AU - Riguzzi, Fabrizio
AU - Swift, Terrance
N1 - Funding Information:
The authors thank Henning Christiansen for his help in validating the experimental results that use removal of non-discriminating arguments. The work of the first author has been partially supported by the Camera di Commercio, Industria, Artigianato e Agricoltura di Ferrara, under the project titled “Image Processing and Artificial Vision for Image Classifications in Industrial Applications”.
Copyright:
Copyright 2013 Elsevier B.V., All rights reserved.
PY - 2011/7
Y1 - 2011/7
N2 - Many real world domains require the representation of a measure of uncertainty. The most common such representation is probability, and the combination of probability with logic programs has given rise to the field of Probabilistic Logic Programming (PLP), leading to languages such as the Independent Choice Logic, Logic Programs with Annotated Disjunctions (LPADs), Problog, PRISM, and others. These languages share a similar distribution semantics, and methods have been devised to translate programs between these languages. The complexity of computing the probability of queries to these general PLP programs is very high due to the need to combine the probabilities of explanations that may not be exclusive. As one alternative, the PRISM system reduces the complexity of query answering by restricting the form of programs it can evaluate. As an entirely different alternative, Possibilistic Logic Programs adopt a simpler metric of uncertainty than probability. Each of these approaches'general PLP, restricted PLP, and Possibilistic Logic Programming'can be useful in different domains depending on the form of uncertainty to be represented, on the form of programs needed to model problems, and on the scale of the problems to be solved. In this paper, we show how the PITA system, which originally supported the general PLP language of LPADs, can also efficiently support restricted PLP and Possibilistic Logic Programs. PITA relies on tabling with answer subsumption and consists of a transformation along with an API for library functions that interface with answer subsumption. We show that, by adapting its transformation and library functions, PITA can be parameterized to PITA(IND, EXC) which supports the restricted PLP of PRISM, including optimizations that reduce non-discriminating arguments and the computation of Viterbi paths. Furthermore, we show PITA to be competitive with PRISM for complex queries to Hidden Markov Model examples, and sometimes much faster. We further show how PITA can be parameterized to PITA(COUNT) which computes the number of different explanations for a subgoal, and to PITA(POSS) which scalably implements Possibilistic Logic Programming. PITA is a supported package in version 3.3 of XSB.
AB - Many real world domains require the representation of a measure of uncertainty. The most common such representation is probability, and the combination of probability with logic programs has given rise to the field of Probabilistic Logic Programming (PLP), leading to languages such as the Independent Choice Logic, Logic Programs with Annotated Disjunctions (LPADs), Problog, PRISM, and others. These languages share a similar distribution semantics, and methods have been devised to translate programs between these languages. The complexity of computing the probability of queries to these general PLP programs is very high due to the need to combine the probabilities of explanations that may not be exclusive. As one alternative, the PRISM system reduces the complexity of query answering by restricting the form of programs it can evaluate. As an entirely different alternative, Possibilistic Logic Programs adopt a simpler metric of uncertainty than probability. Each of these approaches'general PLP, restricted PLP, and Possibilistic Logic Programming'can be useful in different domains depending on the form of uncertainty to be represented, on the form of programs needed to model problems, and on the scale of the problems to be solved. In this paper, we show how the PITA system, which originally supported the general PLP language of LPADs, can also efficiently support restricted PLP and Possibilistic Logic Programs. PITA relies on tabling with answer subsumption and consists of a transformation along with an API for library functions that interface with answer subsumption. We show that, by adapting its transformation and library functions, PITA can be parameterized to PITA(IND, EXC) which supports the restricted PLP of PRISM, including optimizations that reduce non-discriminating arguments and the computation of Viterbi paths. Furthermore, we show PITA to be competitive with PRISM for complex queries to Hidden Markov Model examples, and sometimes much faster. We further show how PITA can be parameterized to PITA(COUNT) which computes the number of different explanations for a subgoal, and to PITA(POSS) which scalably implements Possibilistic Logic Programming. PITA is a supported package in version 3.3 of XSB.
KW - Answer Subsumption
KW - Possibilistic Logic Programming
KW - Probabilistic Logic Programming
KW - Program Transformation
KW - Tabling
UR - http://www.scopus.com/inward/record.url?scp=80054903919&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=80054903919&partnerID=8YFLogxK
U2 - 10.1017/S147106841100010X
DO - 10.1017/S147106841100010X
M3 - Article
AN - SCOPUS:80054903919
VL - 11
SP - 433
EP - 449
JO - Theory and Practice of Logic Programming
JF - Theory and Practice of Logic Programming
SN - 1471-0684
IS - 4-5
ER -