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2014, Latest Advances in Inductive Logic Programming
AI
Probabilistic Inductive Logic Programming (PILP) is becoming increasingly relevant for modeling complex and uncertain relationships among entities. The PITA system provides a method for reasoning under uncertainty in logic programs, utilizing distribution semantics and offering efficient inference capabilities. This paper reviews PITA's framework, compares its performance to that of ProbLog, and demonstrates that PITA achieves faster inference times in various experiments.
Theory and Practice of Logic Programming, 2013
The distribution 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.
The interest in the combination of probability with logics for modeling the world has rapidly increased in the last few years. One of the most effective approaches is the Distribution Semantics which was adopted by many logic programming languages and in Descripion Logics. In this paper, we illustrate the work we have done in this research field by presenting a probabilistic semantics for description logics and reasoning and learning algorithms. In particular, we present in detail the system TRILL P , which computes the probability of queries w.r.t. probabilistic knowledge bases, which has been implemented in Prolog. Note: An extended abstract / full version of a paper accepted to be presented at the Doctoral
2015
Probabilistic logic programming under the distribution semantics has been very useful in machine learning. However, inference is expensive so machine learning algorithms may turn out to be slow. In this paper we consider a restriction of the language called hierarchical PLP in which clauses and predicates are hierarchically organized. In this case the language becomes truth-functional and inference reduces to the evaluation of formulas in the product fuzzy logic. Programs in this language can also be seen as arithmetic circuits or deep neural networks and inference can be reperformed quickly when the parameters change. Learning can then be performed by EM or backpropagation.
Lecture Notes in Computer Science, 2004
In this paper we consider a logic programming framework for reasoning about imprecise probabilities. In particular, we propose a new semantics, for the Probabilistic Logic Programs (p-programs) of Ng and Subrahmanian. Pprograms represent imprecision using probability intervals. Our semantics, based on the possible worlds semantics, considers all point probability distributions that satisfy a given p-program. In the paper, we provide the exact characterization of such models of a p-program. We show that the set of models of a p-program cannot, in general case, be described by single intervals associated with atoms of the program. We provide algorithms for efficient construction of this set of models and study their complexity.
2011
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.
International Journal of Approximate Reasoning, 2017
Lifted inference aims at answering queries from statistical relational models by reasoning on populations of individuals as a whole instead of considering each individual singularly. Since the initial proposal by David Poole in 2003, many lifted inference techniques have appeared, by lifting different algorithms or using approximation involving different kinds of models, including parfactor graphs and Markov Logic Networks. Very recently lifted inference was applied to Probabilistic Logic Programming (PLP) under the distribution semantics, with proposals such as L P 2 and Weighted First-Order Model Counting (WFOMC). Moreover, techniques for dealing with aggregation parfactors can be directly applied to PLP. In this paper we survey these approaches and present an experimental comparison on five models. The results show that WFOMC outperforms the other approaches, being able to exploit more symmetries.
Machine Learning, 2016
We introduce a probabilistic language and an efficient inference algorithm based on distributional clauses for static and dynamic inference in hybrid relational domains. Static inference is based on sampling, where the samples represent (partial) worlds (with discrete and continuous variables). Furthermore, we use backward reasoning to determine which facts should be included in the partial worlds. For filtering in dynamic models we combine the static inference algorithm with particle filters and guarantee that the previous partial samples can be safely forgotten, a condition that does not hold in most logical filtering frameworks. Experiments show that the proposed framework can outperform classic sampling methods for static and dynamic inference and that it is promising for robotics and vision applications. In addition, it provides the correct results in domains in which most probabilistic programming languages fail. Keywords Probabilistic programming • Statistical relational learning • Discrete and continuous distributions • Particle filter • Likelihood weighting • Logic programming Davide Nitti is supported by the IWT (Agentschap voor Innovatie door Wetenschap en Technologie).
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 modedirected 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.
Strict preservation of the (minimum of the) premise probabilities under all (even 'abnormal') probability distributions P loosens this Z and QC loosen also this Strict probability semantics:
Theory and Practice of Logic Programming
In Probabilistic Logic Programming (PLP) the most commonly studied inference task is to compute the marginal probability of a query given a program. In this paper, we consider two other important tasks in the PLP setting: the Maximum-A-Posteriori (MAP) inference task, which determines the most likely values for a subset of the random variables given evidence on other variables, and the Most Probable Explanation (MPE) task, the instance of MAP where the query variables are the complement of the evidence variables. We present a novel algorithm, included in the PITA reasoner, which tackles these tasks by representing each problem as a Binary Decision Diagram and applying a dynamic programming procedure on it. We compare our algorithm with the version of ProbLog that admits annotated disjunctions and can perform MAP and MPE inference. Experiments on several synthetic datasets show that PITA outperforms ProbLog in many cases.
A program in the Probabilistic Logic Programming language ProbLog defines a distribution over possible worlds. Adding evidence (a set of ground probabilistic atoms with observed truth values) rules out some of the possible worlds. Generalizing the evidence atoms to First Order Logic constraints increases the expressive power of ProbLog. In this paper we introduce the first implementation of cProbLog-the extension of ProbLog with constraints. Our implementation transforms ProbLog programs with FOL constraints into ProbLog programs with evidence that specify the same possible worlds. We backup our design and implementation decisions with a series of examples.
Uncertainty Reasoning for the Semantic Web III, 2014
We present a semantics for Probabilistic Description Logics that is based on the distribution semantics for Probabilistic Logic Programming. The semantics, called DISPONTE, allows to express assertional probabilistic statements. We also present two systems for computing the probability of queries to probabilistic knowledge bases: BUNDLE and TRILL. BUNDLE is based on the Pellet reasoner while TRILL exploits the declarative Prolog language. Both algorithms compute a propositional Boolean formula that represents the set of explanations to the query. BUNDLE builds a formula in Disjunctive Normal Form in which each disjunct corresponds to an explanation while TRILL computes a general Boolean pinpointing formula using the techniques proposed by Baader and Peñaloza. Both algorithms then build a Binary Decision Diagram (BDD) representing the formula and compute the probability from the BDD using a dynamic programming algorithm. We also present experiments comparing the performance of BUNDLE and TRILL.
Theory and Practice of Logic Programming, 2011
The past few years have seen a surge of interest in the field of probabilistic logic learning and statistical relational learning. In this endeavor, many probabilistic logics have been developed. ProbLog is a recent probabilistic extension of Prolog motivated by the mining of large biological networks. In ProbLog, facts can be labeled with probabilities. These facts are treated as mutually independent random variables that indicate whether these facts belong to a randomly sampled program. Different kinds of queries can be posed to ProbLog programs. We introduce algorithms that allow the efficient execution of these queries, discuss their implementation on top of the YAP-Prolog system, and evaluate their performance in the context of large networks of biological entities.
2012
Recently much work in Machine Learning has concentrated on using expressive representation languages that combine aspects of logic and probability. A whole field has emerged, called Statistical Relational Learning, rich of successful applications in a variety of domains. In this paper we present a Machine Learning technique targeted to Probabilistic Logic Programs, a family of formalisms where uncertainty is represented using Logic Programming tools. Among various proposals for Probabilistic Logic Programming, the one based on the distribution semantics is gaining popularity and is the basis for languages such as ICL, PRISM, ProbLog and Logic Programs with Annotated Disjunctions. This paper proposes a technique for learning parameters of these languages. Since their equivalent Bayesian networks contain hidden variables, an Expectation Maximization (EM) algorithm is adopted. In order to speed the computation up, expectations are computed directly on the Binary Decision Diagrams that are built for inference. The resulting system, called EMBLEM for "EM over Bdds for probabilistic Logic programs Efficient Mining", has been applied to a number of datasets and showed good performances both in terms of speed and memory usage. In particular its speed allows the execution of a high number of restarts, resulting in good quality of the solutions.
Inductive Logic Programming, 2015
Probabilistic logic languages, such as ProbLog and CP-logic, are probabilistic generalizations of logic programming that allow one to model probability distributions over complex, structured domains. Their key probabilistic constructs are probabilistic facts and annotated disjunctions to represent binary and mutli-valued random variables, respectively. ProbLog allows the use of annotated disjunctions by translating them into probabilistic facts and rules. This encoding is tailored towards the task of computing the marginal probability of a query given evidence (MARG), but is not correct for the task of finding the most probable explanation (MPE) with important applications eg., diagnostics and scheduling. In this work, we propose a new encoding of annotated disjunctions which allows correct MARG and MPE. We explore from both theoretical and experimental perspective the trade-off between the encoding suitable only for MARG inference and the newly proposed (general) approach.
2012 IEEE 42nd International Symposium on Multiple-Valued Logic, 2012
Knowledge representation and inference in AI have been traditionally divided between logic-based and statistical approaches. During the past decade, the rapidly developing area of Statistical Relational Learning aims to combine the two frameworks for representation and inference. In many cases, these works include probabilistic reasoning within Logic Programming frameworks. These attempts are restricted in the sense that they use only two-valued negation-as-failure semantics. However, well-founded semantics is a widely accepted threevalued-logic negation semantics scheme, which is implemented in certain Logic Programming frameworks. In this paper we introduce probabilistic inference under the well-founded semantics scheme in a single Probabilistic Logic Programming framework, where the uncertainty can be described using both statistical information (probabilities) and a third logic value.
2007
Reasoning with qualitative and quantitative uncertainty is required in some real-world applications . However, current extensions to logic programming with uncertainty support representing and reasoning with either qualitative or quantitative uncertainty. In this paper we extend the language of Hybrid Probabilistic Logic programs , originally introduced for reasoning with quantitative uncertainty, to support both qualitative and quantitative uncertainty. We propose to combine disjunctive logic programs with Extended and Normal Hybrid Probabilistic Logic Programs (EHPP [25] and NHPP [28]) in a unified logic programming framework, to allow directly and intuitively to represent and reason in the presence of both qualitative and quantitative uncertainty. The semantics of the proposed languages are based on the answer set semantics and stable model semantics of extended and normal disjunctive logic programs . In addition, they also rely on the probabilistic answer set semantics and the stable probabilistic model semantics of EHPP [25] and NHPP .
2016
Probabilistic logic programs without negation can have cycles (with a preference for false), but cannot represent all conditional distributions. Probabilistic logic programs with negation can represent arbitrary conditional probabilities, but with cycles they create logical inconsistencies. We show how allowing negative noise probabilities allows us to represent arbitrary conditional probabilities without negations. Noise probabilities for non-exclusive rules are difficult to interpret and unintuitive to manipulate; to alleviate this we define "probability-strengths" which provide an intuitive additive algebra for combining rules. For acyclic programs we prove what constraints on the strengths allow for proper distributions on the non-noise variables and allow for all non-extreme distributions to be represented. We show how arbitrary CPDs can be converted into this form in a canonical way. Furthermore, if a joint distribution can be compactly represented by a cyclic progra...
1995
We present a probabilistic logic programming framework that allows the representation of conditional probabilities. While conditional probabilities are the most commonly used method for representing uncertainty in probabilistic expert systems, they have been largely neglected by work in quantitative logic programming. We define a fixpoint theory, declarative semantics, and proof procedure for the new class of probabilistic logic programs. Compared to other approaches to quantitative logic programming, we provide a true probabilistic framework with potential applications in probabilistic expert systems and decision support systems. We also discuss the relationship between such programs and Bayesian networks, thus moving toward a unification of two major approaches to automated reasoning.
2011
We present DISPONTE, a semantics for probabilistic ontologies that is based on the distribution semantics for probabilistic logic programs. In DISPONTE each axiom of a probabilistic ontology is annotated with a probability. The probabilistic theory defines thus a distribution over normal theories (called worlds) obtained by including an axiom in a world with a probability given by the annotation. The probability of a query is computed from this distribution with marginalization. We also present the system BUNDLE for reasoning over probabilistic OWL DL ontologies according to the DISPONTE semantics. BUNDLE is based on Pellet and uses its capability of returning explanations for a query. The explanations are encoded in a Binary Decision Diagram from which the probability of the query is computed.
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