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The PITA System: Tabling and Answer Subsumption for Reasoning under Uncertainty
 UNDER CONSIDERATION FOR PUBLICATION IN THEORY AND PRACTICE OF LOGIC PROGRAMMING
, 2003
"... Many 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 Independen ..."
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Many 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 IndependentChoice 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
Modedirected tabling for dynamic programming, machine learning, and constraint solving
 In Proceedings of the International Conference on Tools with Artificial Intelligence (ICTAI
"... Abstract—The abstract goes here. Tabling [12], [13], [15] has been found increasingly important for not only helping beginners write workable declarative programs but also developing realworld applications such as natural language processing, model checking, and machine ..."
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Abstract—The abstract goes here. Tabling [12], [13], [15] has been found increasingly important for not only helping beginners write workable declarative programs but also developing realworld applications such as natural language processing, model checking, and machine
Speeding Up Inference for Probabilistic Logic Programs
"... Probabilistic Logic Programming (PLP) allows to represent domains containing many entities connected by uncertain relations and has many applications in particular in Machine Learning. PITA is a PLP algorithm for computing the probability of queries that exploits tabling, answer subsumption and Bina ..."
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Cited by 2 (1 self)
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Probabilistic Logic Programming (PLP) allows to represent domains containing many entities connected by uncertain relations and has many applications in particular in Machine Learning. PITA is a PLP algorithm for computing the probability of queries that exploits tabling, answer subsumption and Binary Decision Diagrams (BDDs). PITA does not impose any restriction on the programs. Other algorithms, such as PRISM, reduce computation time by imposing restrictions on the program, namely that subgoals are independent and that clause bodies are mutually exclusive. Another assumption that simplifies inference is that clause bodies are independent. In this paper we present the algorithms PITA(IND,IND) and PITA(OPT). PITA(IND,IND) assumes that subgoals and clause bodies are independent. PITA(OPT) instead first checks whether these assumptions hold for subprograms and subgoals: if they do, PITA(OPT) uses a simplified calculation, otherwise it resorts to BDDs. Experiments on a number of benchmark datasets show that PITA(IND,IND) is the fastest on datasets respecting the assumptions while PITA(OPT) is a good option when nothing is known about a dataset.
M.: Inference with Constrained Hidden Markov Models
 in PRISM (2010), accepted for ICLP 2010, Int’l Conf. on Logic Programming; to appear in Theory and Practice of Logic Programming
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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
MCINTYRE: A Monte Carlo Algorithm for Probabilistic Logic Programming
"... Abstract. Probabilistic Logic Programming is receiving an increasing attention for its ability to model domains with complex and uncertain relations among entities. In this paper we concentrate on the problem of approximate inference in probabilistic logic programming languages based on the distribu ..."
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Abstract. Probabilistic Logic Programming is receiving an increasing attention for its ability to model domains with complex and uncertain relations among entities. In this paper we concentrate on the problem of approximate inference in probabilistic logic programming languages based on the distribution semantics. A successful approximate approach is based on Monte Carlo sampling, that consists in verifying the truth of the query in a normal program sampled from the probabilistic program. The ProbLog system includes such an algorithm and so does the cplint suite. In this paper we propose an approach for Monte Carlo inference that is based on a program transformation that translates a probabilistic program into a normal program to which the query can be posed. In the transformation, auxiliary atoms are added to the body of rules for performing sampling and checking for the consistency of the sample. The current sample is stored in the internal database of the Yap Prolog engine. The resulting algorithm, called MCINTYRE for Monte Carlo INference wiTh Yap REcord, is evaluated on various problems: biological networks, artificial datasets and a hidden Markov model. MCINTYRE is compared with the Monte Carlo algorithms of ProbLog and cplint and with the exact inference of the PITA system. The results show that MCINTYRE is faster than the other Monte Carlo algorithms.
A Logicbased Approach to Generatively Defined Discriminative Modeling
"... Abstract. Conditional random fields (CRFs) are usually specified by graphical models but in this paper we propose to use probabilistic logic programs and specify them generatively. Our intension is first to provide a unified approach to CRFs for complex modeling through the use of a Turing complete ..."
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Abstract. Conditional random fields (CRFs) are usually specified by graphical models but in this paper we propose to use probabilistic logic programs and specify them generatively. Our intension is first to provide a unified approach to CRFs for complex modeling through the use of a Turing complete language and second to offer a convenient way of realizing generativediscriminative pairs in machine learning. We implemented our approach as the DPRISM language by modifying PRISM, a logicbased probabilistic modeling language for generative modeling, while exploiting its dynamic programming mechanism for efficient probability computation. We tested DPRISM with logistic regression, a linearchain CRF and a CRFCFG and empirically confirmed their excellent discriminative performance compared to their generative counterparts, i.e. naive Bayes, an HMM and a PCFG. 1
Under consideration for publication in Theory and Practice of Logic Programming 1 XSB: Extending Prolog with Tabled Logic Programming
, 2003
"... The paradigm of Tabled Logic Programming (TLP) is now supported by a number of Prolog systems, including XSB, YAP, B Prolog, Mercury, ALS, and Ciao. The reasons for this are partly theoretical: tabling ensures termination and optimal known complexity for queries to a large class of programs. However ..."
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The paradigm of Tabled Logic Programming (TLP) is now supported by a number of Prolog systems, including XSB, YAP, B Prolog, Mercury, ALS, and Ciao. The reasons for this are partly theoretical: tabling ensures termination and optimal known complexity for queries to a large class of programs. However the overriding reasons are practical. TLP allows sophisticated programs to be written concisely and efficiently, especially when mechanisms such as tabled negation and call and answer subsumption are supported. As a result TLP has now been used in a variety of applications from program analysis to querying over the semantic web. This paper provides a survey of TLP and its applications as implemented in XSB Prolog, along with discussion of how XSB supports tabling with