Tabling and Answer Subsumption for Reasoning on Logic Programs with Annotated Disjunctions

Abstract Probabilistic Logic Programming is an active field of research, with many proposals for languages, semantics and reasoning algorithms. One such proposal, Logic Programming with Annotated Disjunctions (LPADs) represents probabilistic information in a sound and simple way. This paper presents the algorithm "Probabilistic Inference with Tabling and Answer subsumption" (PITA) for computing the probability of queries. Answer subsumption is a feature of tabling that allows the combination of different answers for the same subgoal in the case in which a partial order can be defined over them. We have applied it in our case since probabilistic explanations (stored as BDDs in PITA) possess a natural lattice structure. PITA has been implemented in XSB and compared with ProbLog, cplint and CVE. The results show that, in almost all cases, PITA is able to solve larger problems and is faster than competing algorithms

The PITA System: Tabling and Answer Subsumption for Reasoning under Uncertainty

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

Probabilistic inference in SWI-Prolog

Probabilistic Logic Programming (PLP) emerged as one of the most prominent approaches to cope with real-world domains. The distribution semantics is one of most used in PLP, as it is followed by many languages, such as Independent Choice Logic, PRISM, pD, Logic Programs with Annotated Disjunctions (LPADs) and ProbLog. A possible system that allows performing inference on LPADs is PITA, which transforms the input LPAD into a Prolog program containing calls to library predicates for handling Binary Decision Diagrams (BDDs). In particular, BDDs are used to compactly encode explanations for goals and efficiently compute their probability. However, PITA needs mode-directed tabling (also called tabling with answer subsumption), which has been implemented in SWI-Prolog only recently. This paper shows how SWI-Prolog has been extended to include correct answer subsumption and how the PITA transformation has been changed to use SWI-Prolog implementation

Nesting Probabilistic Inference

When doing inference in ProbLog, a probabilistic extension of Prolog, we extend SLD resolution with some additional bookkeeping. This additional information is used to compute the probabilistic results for a probabilistic query. In Prolog's SLD, goals are nested very naturally. In ProbLog's SLD, nesting probabilistic queries interferes with the probabilistic bookkeeping. In order to support nested probabilistic inference we propose the notion of a parametrised ProbLog engine. Nesting becomes possible by suspending and resuming instances of ProbLog engines. With our approach we realise several extensions of ProbLog such as meta-calls, negation, and answers of probabilistic goals.Comment: Online Proceedings of the 11th International Colloquium on Implementation of Constraint LOgic Programming Systems (CICLOPS 2011), Lexington, KY, U.S.A., July 10, 201

Inference in Probabilistic Logic Programs with Continuous Random Variables

Probabilistic Logic Programming (PLP), exemplified by Sato and Kameya's PRISM, Poole's ICL, Raedt et al's ProbLog and Vennekens et al's LPAD, is aimed at combining statistical and logical knowledge representation and inference. A key characteristic of PLP frameworks is that they are conservative extensions to non-probabilistic logic programs which have been widely used for knowledge representation. PLP frameworks extend traditional logic programming semantics to a distribution semantics, where the semantics of a probabilistic logic program is given in terms of a distribution over possible models of the program. However, the inference techniques used in these works rely on enumerating sets of explanations for a query answer. Consequently, these languages permit very limited use of random variables with continuous distributions. In this paper, we present a symbolic inference procedure that uses constraints and represents sets of explanations without enumeration. This permits us to reason over PLPs with Gaussian or Gamma-distributed random variables (in addition to discrete-valued random variables) and linear equality constraints over reals. We develop the inference procedure in the context of PRISM; however the procedure's core ideas can be easily applied to other PLP languages as well. An interesting aspect of our inference procedure is that PRISM's query evaluation process becomes a special case in the absence of any continuous random variables in the program. The symbolic inference procedure enables us to reason over complex probabilistic models such as Kalman filters and a large subclass of Hybrid Bayesian networks that were hitherto not possible in PLP frameworks. (To appear in Theory and Practice of Logic Programming).Comment: 12 pages. arXiv admin note: substantial text overlap with arXiv:1203.428