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 Inference and learning in probabilistic logic programs using weighted Boolean formulas

2014 ◽  
Vol 15 (3) ◽  
pp. 358-401 ◽  
Author(s):  
DAAN FIERENS ◽  
GUY VAN DEN BROECK ◽  
JORIS RENKENS ◽  
DIMITAR SHTERIONOV ◽  
BERND GUTMANN ◽  
...  
Keyword(s):  
Graphical Model ◽  
State Of The Art ◽  
Logic Program ◽  
Knowledge Compilation ◽  
Boolean Formula ◽  
Probabilistic Logic ◽  
Logic Programs ◽  
Inference Algorithms ◽  
Boolean Formulas ◽  
Model Counting

AbstractProbabilistic logic programs are logic programs in which some of the facts are annotated with probabilities. This paper investigates how classical inference and learning tasks known from the graphical model community can be tackled for probabilistic logic programs. Several such tasks, such as computing the marginals, given evidence and learning from (partial) interpretations, have not really been addressed for probabilistic logic programs before. The first contribution of this paper is a suite of efficient algorithms for various inference tasks. It is based on the conversion of the program and the queries and evidence to a weighted Boolean formula. This allows us to reduce inference tasks to well-studied tasks, such as weighted model counting, which can be solved using state-of-the-art methods known from the graphical model and knowledge compilation literature. The second contribution is an algorithm for parameter estimation in the learning from interpretations setting. The algorithm employs expectation-maximization, and is built on top of the developed inference algorithms. The proposed approach is experimentally evaluated. The results show that the inference algorithms improve upon the state of the art in probabilistic logic programming, and that it is indeed possible to learn the parameters of a probabilistic logic program from interpretations.

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 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 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 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.

scholarly journals Learning Large Logic Programs By Going Beyond Entailment

2020 ◽  
Author(s):  
Andrew Cropper ◽  
Sebastijan Dumančic
Keyword(s):  
Logic Programming ◽  
Loss Function ◽  
Inductive Logic Programming ◽  
State Of The Art ◽  
Inductive Logic ◽  
Program Synthesis ◽  
Loss Functions ◽  
Logic Programs ◽  
Binary Decision ◽  
Best First Search

A major challenge in inductive logic programming (ILP) is learning large programs. We argue that a key limitation of existing systems is that they use entailment to guide the hypothesis search. This approach is limited because entailment is a binary decision: a hypothesis either entails an example or does not, and there is no intermediate position. To address this limitation, we go beyond entailment and use 'example-dependent' loss functions to guide the search, where a hypothesis can partially cover an example. We implement our idea in Brute, a new ILP system which uses best-first search, guided by an example-dependent loss function, to incrementally build programs. Our experiments on three diverse program synthesis domains (robot planning, string transformations, and ASCII art), show that Brute can substantially outperform existing ILP systems, both in terms of predictive accuracies and learning times, and can learn programs 20 times larger than state-of-the-art systems.

Abduction with Probabilistic Logic Programming under the Distribution Semantics

2021 ◽  
Author(s):  
Damiano Azzolini ◽  
Elena Bellodi ◽  
Stefano Ferilli ◽  
Fabrizio Riguzzi ◽  
Riccardo Zese
Keyword(s):  
Logic Programming ◽  
Probabilistic Logic ◽  
Probabilistic Logic Programming ◽  
Distribution Semantics

scholarly journals ProbLog2: Probabilistic Logic Programming

2015 ◽  
pp. 312-315 ◽  
Author(s):  
Anton Dries ◽  
Angelika Kimmig ◽  
Wannes Meert ◽  
Joris Renkens ◽  
Guy Van den Broeck ◽  
...  
Keyword(s):  
Logic Programming ◽  
Probabilistic Logic ◽  
Probabilistic Logic Programming

scholarly journals Induction of Non-Monotonic Logic Programs to Explain Boosted Tree Models Using LIME

2019 ◽  
Vol 33 ◽  
pp. 3052-3059 ◽  
Author(s):  
Farhad Shakerin ◽  
Gopal Gupta
Keyword(s):  
Logic Programming ◽  
Inductive Logic Programming ◽  
State Of The Art ◽  
Inductive Logic ◽  
Nonmonotonic Logic ◽  
Global Behavior ◽  
Logic Programs ◽  
Tree Models ◽  
Boosted Tree ◽  
Classification Evaluation

We present a heuristic based algorithm to induce nonmonotonic logic programs that will explain the behavior of XGBoost trained classifiers. We use the technique based on the LIME approach to locally select the most important features contributing to the classification decision. Then, in order to explain the model’s global behavior, we propose the LIME-FOLD algorithm —a heuristic-based inductive logic programming (ILP) algorithm capable of learning nonmonotonic logic programs—that we apply to a transformed dataset produced by LIME. Our proposed approach is agnostic to the choice of the ILP algorithm. Our experiments with UCI standard benchmarks suggest a significant improvement in terms of classification evaluation metrics. Meanwhile, the number of induced rules dramatically decreases compared to ALEPH, a state-of-the-art ILP system.

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