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Inference and learning in probabilistic logic programs using weighted Boolean formulas

arXiv.org Artificial Intelligence

Probabilistic 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 a conversion of the program and the queries and evidence to a weighted Boolean formula. This allows us to reduce the 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.


Knowledge Compilation and Weighted Model Counting for Inference in Probabilistic Logic Programs

AAAI Conferences

Over the last decade, building on advances in the areas of knowledge compilation and weighted model counting has drastically increased the scalability of inference in probabilistic logic programs. In this paper, we provide an overview of how this has been possible and point out some open challenges.


Situation Calculus Based Programs for Representing and Reasoning about Game Structures

AAAI Conferences

A wide range of problems, from contingent and multiagent planning to process/service orchestration, can be viewed as games. In many of these, it is natural to spec- ify the possible behaviors procedurally. In this paper, we develop a logical framework for specifying these types of problems/games based on the situation calculus and ConGolog. The framework incorporates game-theoretic path quantifiers as in ATL. We show that the framework can be used to model such problems in a natural way. We also show how verification/synthesis techniques can be used to solve problems expressed in the framework. In particular, we develop a method for dealing with infinite state settings using fixpoint approximation and “characteristic graphs”.


AAAI08-075.pdf

AAAI Conferences

In a recent paper, Ferraris, Lee and Lifschitz conjectured that the concept of a stable model of a first-order formula can be used to treat some answer set programming expressions as abbreviations. We follow up on that suggestion and introduce an answer set programming language that defines the meaning of counting and choice by reducing these constructs to first-order formulas. For the new language, the concept of a safe program is defined, and its semantic role is investigated.


Bounds on the size of PC and URC formulas

arXiv.org Artificial Intelligence

In this paper we investigate CNF formulas, for which the unit propagation is strong enough to derive a contradiction if the formula together with a partial assignment of the variables is unsatisfiable (unit refutation complete or URC formulas) or additionally to derive all implied literals if the formula is satisfiable (propagation complete or PC formulas). If a formula represents a function using existentially quantified auxiliary variables, it is called an encoding of the function. We prove several results on the sizes of PC and URC formulas and encodings. One of them are separations between the sizes of formulas of different types. Namely, we prove an exponential separation between the size of URC formulas and PC formulas and between the size of PC encodings using auxiliary variables and URC formulas. Besides of this, we prove that the sizes of any two irredundant PC formulas for the same function differ at most by a polynomial factor in the number of the variables and present an example of a function demonstrating that a similar statement is not true for URC formulas. One of the separations above implies that a q-Horn formula may require an exponential number of additional clauses to become a URC formula. On the other hand, for every q-Horn formula, we present a polynomial size URC encoding of the same function using auxiliary variables. This encoding is not q-Horn in general.