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Expectation Maximization over Binary Decision Diagrams for Probabilistic Logic Programs
"... 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 M ..."
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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 andLogic 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.
Tabling and Answer Subsumption for Reasoning on Logic Programs with Annotated Disjunctions
 In Technical Communications of the International Conference on Logic Programming. LIPIcs, vol. 7. Schloss Dagstuhl– LeibnizZentrum fuer Informatik
"... 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 present ..."
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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.
LogicBased Decision Support for Strategic Environmental Assessment. Theory and Practice
 of Logic Programming, 26th Int’l. Conference on Logic Programming (ICLP’10) Special Issue
, 2010
"... Abstract Strategic Environmental Assessment is a procedure aimed at introducing systematic assessment of the environmental effects of plans and programs. This procedure is based on the socalled coaxial matrices that define dependencies between plan activities (infrastructures, plants, resource extr ..."
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Abstract Strategic Environmental Assessment is a procedure aimed at introducing systematic assessment of the environmental effects of plans and programs. This procedure is based on the socalled coaxial matrices that define dependencies between plan activities (infrastructures, plants, resource extractions, buildings, etc.) and positive and negative environmental impacts, and dependencies between these impacts and environmental receptors. Up to now, this procedure is manually implemented by environmental experts for checking the environmental effects of a given plan or program, but it is never applied during the plan/program construction. A decision support system, based on a clear logic semantics, would be an invaluable tool not only in assessing a single, already defined plan, but also during the planning process in order to produce an optimized, environmentally assessed plan and to study possible alternative scenarios. We propose two logicbased approaches to the problem, one based on Constraint Logic Programming and one on Probabilistic Logic Programming that could be, in the future, conveniently merged to exploit the advantages of both. We test the proposed approaches on a real energy plan and we discuss their limitations and advantages.
F.: Learning the structure of probabilistic logic programs
 ILP 2011. LNCS
, 2012
"... Abstract. There is a growing interest in the field of Probabilistic Inductive Logic Programming, which uses languages that integrate logic programming and probability. Many of these languages are based on the distribution semantics and recently various authors have proposed systems for learning the ..."
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Abstract. There is a growing interest in the field of Probabilistic Inductive Logic Programming, which uses languages that integrate logic programming and probability. Many of these languages are based on the distribution semantics and recently various authors have proposed systems for learning the parameters (PRISM, LeProbLog, LFIProbLog and EMBLEM) or both the structure and the parameters (SEMCPlogic) of these languages. EMBLEM for example uses an Expectation Maximization approach in which the expectations are computed on Binary Decision Diagrams. In this paper we present the algorithm SLIPCASE for “Structure LearnIng of ProbabilistiC logic progrAmS with Em over bdds”. It performs a beam search in the space of the language of Logic Programs with Annotated Disjunctions (LPAD) using the log likelihood of the data as the guiding heuristics. To estimate the log likelihood of theory refinements it performs a limited number of Expectation Maximization iterations of EMBLEM. SLIPCASE has been tested on three realworld datasetsandcomparedwithSEMCPlogic andLearningusing Structural Motifs, an algorithm for Markov Logic Networks. The results show that SLIPCASE achieves higher areas under the precisionrecall and ROC curves and is more scalable.
Towards (Probabilistic) Argumentation for Jurybased Dispute Resolution," COMMA 2010
"... Abstract. We propose an argumentation framework for modelling jurybased dispute resolution where the dispute parties present their arguments before a judge and a jury. While the judge as the arbiter of law determines the legal permissibility of the presented arguments the jurors as triers of facts ..."
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Abstract. We propose an argumentation framework for modelling jurybased dispute resolution where the dispute parties present their arguments before a judge and a jury. While the judge as the arbiter of law determines the legal permissibility of the presented arguments the jurors as triers of facts determine their probable weights. Such a framework is based on two key components: classical argumentation frameworks containing legally permissible arguments and probabilistic spaces assigning probable weights to arguments. A juror's probability space is represented by a set of possible worlds coupled with a probabilistic measure computed by assumptionbased argumentation framework using grounded semantics.
The Magic of Logical Inference in Probabilistic Programming
 UNDER CONSIDERATION FOR PUBLICATION IN THEORY AND PRACTICE OF LOGIC PROGRAMMING
, 2011
"... Today, many different probabilistic programming languages exist and even more inference mechanisms for these languages. Still, most logic programming based languages use backward reasoning based on SLD resolution for inference. While these methods are typically computationally efficient, they often ..."
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Cited by 6 (0 self)
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Today, many different probabilistic programming languages exist and even more inference mechanisms for these languages. Still, most logic programming based languages use backward reasoning based on SLD resolution for inference. While these methods are typically computationally efficient, they often can neither handle infinite and/or continuous distributions, nor evidence. To overcome these limitations, we introduce distributional clauses, a variation and extension of Sato’s distribution semantics. We also contribute a novel approximate inference method that integrates forward reasoning with importance sampling, a wellknown technique for probabilistic inference. To achieve efficiency, we integrate two logic programming techniques to direct forward sampling. Magic sets are used to focus on relevant parts of the program, while the integration of backward reasoning allows one to identify and avoid regions of the sample space that are inconsistent with the evidence.
Structure learning of probabilistic logic programs by searching the clause space
 CoRR/arXiv:1309.2080
, 2013
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An abductive counterfactual reasoning approach in logic programming. Available from http://goo.gl/bx0mIZ
, 2015
"... We construct a counterfactual statement when we reason conjecturally about an event which did or did not occur in the past: If an event had occurred, what would have happened? Would it be relevant? Real world examples, as studied by Byrne, Rescher and many others, show that these conditionals invol ..."
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We construct a counterfactual statement when we reason conjecturally about an event which did or did not occur in the past: If an event had occurred, what would have happened? Would it be relevant? Real world examples, as studied by Byrne, Rescher and many others, show that these conditionals involve a complex reasoning process. An intuitive and elegant approach to evaluate counterfactuals, without deep revision mechanisms, is proposed by Pearl. His DoCalculus identifies causal relations in a Bayesian network resorting to counterfactuals. Though leaving out probabilities, we adopt Pearl’s stance, and its prior epistemological justification to counterfactuals in causal Bayesian networks, but for programs. Logic programming seems a suitable environment for several reasons. First, its inferential arrow is adept at expressing causal direction and conditional reasoning. Secondly, together with its other functionalities such as abduction, integrity constraints, revision, updating and debugging (a form of counterfactual reasoning), it proffers a wide range of expressibility itself. We show here how programs under the weak completion semantics in an abductive framework, comprising the integrity constraints, can smoothly and uniformly capture wellknown and offtheshelf counterfactual problems and conundrums, taken from the psychological and philosophical literature. Our approach is adroitly reconstructable in other threevalued LP semantics, or restricted to twovalued ones.
Inference in probabilistic logic programs with continuous random variables, Theory Pract
 Log. Program
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Model Checking with Probabilistic Tabled Logic Programming∗
"... We present a formulation of the problem of probabilistic model checking as one of query evaluation over probabilistic logic programs. To the best of our knowledge, our formulation is the first of its kind, and it covers a rich class of probabilistic models and probabilistic temporal logics. The infe ..."
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We present a formulation of the problem of probabilistic model checking as one of query evaluation over probabilistic logic programs. To the best of our knowledge, our formulation is the first of its kind, and it covers a rich class of probabilistic models and probabilistic temporal logics. The inference algorithms of existing probabilistic logicprogramming systems are well defined only for queries with a finite number of explanations. This restriction prohibits the encoding of probabilistic model checkers, where explanations correspond to executions of the system being model checked. To overcome this restriction, we propose a more general inference algorithm that uses finite generative structures (similar to automata) to represent families of explanations. The inference algorithm computes the probability of a possibly infinite set of explanations directly from the finite generative structure. We have implemented our inference algorithm in XSB Prolog, and use this implementation to encode probabilistic model checkers for a variety of temporal logics, including PCTL and GPL (which subsumes PCTL∗). Our experiment results show that, despite the highly declarative nature of their encodings, the model checkers constructed in this manner are competitive with their native implementations. 1