scholarly journals An Asymptotic Analysis of Probabilistic Logic Programming, with Implications for Expressing Projective Families of Distributions

2021 ◽  
pp. 1-16
Author(s):  
FELIX Q. WEITKÄMPER
Keyword(s):  
Logic Programming ◽  
Size Dependence ◽  
Logic Program ◽  
Domain Size ◽  
Probabilistic Logic ◽  
Logic Programs ◽  
Probabilistic Logic Programming ◽  
Lifted Inference ◽  
Relational Domains ◽  
Distribution Semantics

Abstract Probabilistic logic programming is a major part of statistical relational artificial intelligence, where approaches from logic and probability are brought together to reason about and learn from relational domains in a setting of uncertainty. However, the behaviour of statistical relational representations across variable domain sizes is complex, and scaling inference and learning to large domains remains a significant challenge. In recent years, connections have emerged between domain size dependence, lifted inference and learning from sampled subpopulations. The asymptotic behaviour of statistical relational representations has come under scrutiny, and projectivity was investigated as the strongest form of domain size dependence, in which query marginals are completely independent of the domain size. In this contribution we show that every probabilistic logic program under the distribution semantics is asymptotically equivalent to an acyclic probabilistic logic program consisting only of determinate clauses over probabilistic facts. We conclude that every probabilistic logic program inducing a projective family of distributions is in fact everywhere equivalent to a program from this fragment, and we investigate the consequences for the projective families of distributions expressible by probabilistic logic programs.

scholarly journals Lifted Variable Elimination for Probabilistic Logic Programming

2014 ◽  
Vol 14 (4-5) ◽  
pp. 681-695 ◽  
Author(s):  
ELENA BELLODI ◽  
EVELINA LAMMA ◽  
FABRIZIO RIGUZZI ◽  
VITOR SANTOS COSTA ◽  
RICCARDO ZESE
Keyword(s):  
Logic Programming ◽  
Random Variables ◽  
Probabilistic Logic ◽  
Probabilistic Logic Programming ◽  
Lifted Inference ◽  
Logical Frameworks ◽  
Variable Elimination ◽  
Causal Independence ◽  
Order Variable ◽  
Distribution Semantics

AbstractLifted 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 LP2for 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.

scholarly journals Well–definedness and efficient inference for probabilistic logic programming under the distribution semantics

2012 ◽  
Vol 13 (2) ◽  
pp. 279-302 ◽  
Author(s):  
FABRIZIO RIGUZZI ◽  
TERRANCE SWIFT
Keyword(s):  
Probability Theory ◽  
Logic Programming ◽  
Probabilistic Inference ◽  
Probabilistic Logic ◽  
Logic Programs ◽  
Efficient Procedure ◽  
Probabilistic Logic Programming ◽  
Execution Times ◽  
Distribution Semantics

AbstractDistribution semantics is one of the most prominent approaches for the combination of logic programming and probability theory. Many languages follow this semantics, such as Independent Choice Logic, PRISM, pD, Logic Programs with Annotated Disjunctions (LPADs), and ProbLog. When a program contains functions symbols, the distribution semantics is well–defined only if the set of explanations for a query is finite and so is each explanation. Well–definedness is usually either explicitly imposed or is achieved by severely limiting the class of allowed programs. In this paper, we identify a larger class of programs for which the semantics is well–defined together with an efficient procedure for computing the probability of queries. Since Logic Programs with Annotated Disjunctions offer the most general syntax, we present our results for them, but our results are applicable to all languages under the distribution semantics. We present the algorithm “Probabilistic Inference with Tabling and Answer subsumption” (PITA) that computes the probability of queries by transforming a probabilistic program into a normal program and then applying SLG resolution with answer subsumption. PITA has been implemented in XSB and tested on six domains: two with function symbols and four without. The execution times are compared with those of ProbLog, cplint, and CVE. PITA was almost always able to solve larger problems in a shorter time, on domains with and without function symbols.

scholarly journals Learning hierarchical probabilistic logic programs

2021 ◽  
Author(s):  
Arnaud Nguembang Fadja ◽  
Fabrizio Riguzzi ◽  
Evelina Lamma
Keyword(s):  
Logic Programming ◽  
Expectation Maximization ◽  
Gradient Descent ◽  
Structure Learning ◽  
Probabilistic Logic ◽  
Logic Programs ◽  
Markov Logic Networks ◽  
Markov Logic ◽  
Probabilistic Logic Programming ◽  
Relational Domains

AbstractProbabilistic logic programming (PLP) combines logic programs and probabilities. Due to its expressiveness and simplicity, it has been considered as a powerful tool for learning and reasoning in relational domains characterized by uncertainty. Still, learning the parameter and the structure of general PLP is computationally expensive due to the inference cost. We have recently proposed a restriction of the general PLP language called hierarchical PLP (HPLP) in which clauses and predicates are hierarchically organized. HPLPs can be converted into arithmetic circuits or deep neural networks and inference is much cheaper than for general PLP. In this paper we present algorithms for learning both the parameters and the structure of HPLPs from data. We first present an algorithm, called parameter learning for hierarchical probabilistic logic programs (PHIL) which performs parameter estimation of HPLPs using gradient descent and expectation maximization. We also propose structure learning of hierarchical probabilistic logic programming (SLEAHP), that learns both the structure and the parameters of HPLPs from data. Experiments were performed comparing PHIL and SLEAHP with PLP and Markov Logic Networks state-of-the art systems for parameter and structure learning respectively. PHIL was compared with EMBLEM, ProbLog2 and Tuffy and SLEAHP with SLIPCOVER, PROBFOIL+, MLB-BC, MLN-BT and RDN-B. The experiments on five well known datasets show that our algorithms achieve similar and often better accuracies but in a shorter time.

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

2011 ◽  
Vol 11 (4-5) ◽  
pp. 433-449 ◽  
Author(s):  
FABRIZIO RIGUZZI ◽  
TERRANCE SWIFT
Keyword(s):  
Logic Programming ◽  
Probabilistic Logic ◽  
Similar Distribution ◽  
Logic Programs ◽  
Reasoning Under Uncertainty ◽  
Complex Queries ◽  
Possibilistic Logic ◽  
Distribution Semantics ◽  
Measure Of Uncertainty ◽  
Very High

AbstractMany 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.

scholarly journals Probabilistic logic programming for hybrid relational domains

2016 ◽  
Vol 103 (3) ◽  
pp. 407-449 ◽  
Author(s):  
Davide Nitti ◽  
Tinne De Laet ◽  
Luc De Raedt
Keyword(s):  
Logic Programming ◽  
Probabilistic Logic ◽  
Probabilistic Logic Programming ◽  
Relational Domains

scholarly journals Beyond the Grounding Bottleneck: Datalog Techniques for Inference in Probabilistic Logic Programs

2020 ◽  
Vol 34 (06) ◽  
pp. 10284-10291
Author(s):  
Efthymia Tsamoura ◽  
Victor Gutierrez-Basulto ◽  
Angelika Kimmig
Keyword(s):  
Logic Programming ◽  
State Of The Art ◽  
Knowledge Compilation ◽  
Probabilistic Logic ◽  
Logic Programs ◽  
Probabilistic Logic Programming ◽  
Forward Reasoning ◽  
Alternative Approach ◽  
Model Counting ◽  
Weighted Model

State-of-the-art inference approaches in probabilistic logic programming typically start by computing the relevant ground program with respect to the queries of interest, and then use this program for probabilistic inference using knowledge compilation and weighted model counting. We propose an alternative approach that uses efficient Datalog techniques to integrate knowledge compilation with forward reasoning with a non-ground program. This effectively eliminates the grounding bottleneck that so far has prohibited the application of probabilistic logic programming in query answering scenarios over knowledge graphs, while also providing fast approximations on classical benchmarks in the field.

scholarly journals Optimizing Probabilities in Probabilistic Logic Programs

2021 ◽  
pp. 1-14
Author(s):  
DAMIANO AZZOLINI ◽  
FABRIZIO RIGUZZI
Keyword(s):  
Logic Programming ◽  
Objective Function ◽  
Probability Distributions ◽  
Random Variables ◽  
Probabilistic Logic ◽  
Effective Algorithm ◽  
Logic Programs ◽  
Probabilistic Logic Programming ◽  
New Class

Abstract Probabilistic logic programming is an effective formalism for encoding problems characterized by uncertainty. Some of these problems may require the optimization of probability values subject to constraints among probability distributions of random variables. Here, we introduce a new class of probabilistic logic programs, namely probabilistic optimizable logic programs, and we provide an effective algorithm to find the best assignment to probabilities of random variables, such that a set of constraints is satisfied and an objective function is optimized.

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