The PITA system: Tabling and answer subsumption for reasoning under uncertainty

Abstract

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. F. Riguzzi and T. Swift

An OpenCL implementation of a forward sampling algorithm for CP-logic

“…• The approach of [9], which transforms CP-logic into a Bayesian network and then applies the Variable Elimination (VE) algorithm or Contextual Variable Elimination (CVE) [10] • The default and Monte Carlo inference algorithms of the ProbLog system [7] • The PITA algorithm [18] that is built into XSB Prolog • The MCINTYRE backwards sampling algorithms [15].…”

TP-Compilation for inference in probabilistic logic programs

“…Knowledge compilation and weighted model counting has shown to be very effective for inference in probabilistic logic programs (De Raedt et al, 2007;Riguzzi, 2007;Riguzzi and Swift, 2011;Fierens et al, 2015) as well as graphical models (Chavira and Darwiche, 2005;Darwiche, 2009;Choi et al, 2013). Exact compilation of a propositional formula is computational expensive, however, and one often has to resort to approximate techniques.…”

Value of Information in Probabilistic Logic Programs

“…Probabilistic Logic Programs (PLPs) have been proposed as an expressive mechanism to model and reason about systems combining logical and statistical knowledge. Programming languages and systems studied under the framework of PLP include PRISM [21], Problog [2], PITA [20] and Problog2 [6]. These languages have similar declarative semantics based on the distribution semantics [22].…”