We present a probabilistic extension of action language BC+. Just like BC+ is defined as a high-level notation of answer set programs for describing transition systems, the proposed language, which we call pBC+, is defined as a high-level notation of LPMLN programs---a probabilistic extension of answer set programs. We show how probabilistic reasoning about transition systems, such as prediction, postdiction, and planning problems, as well as probabilistic diagnosis for dynamic domains, can be modeled in pBC+ and computed using an implementation of LPMLN.
@math is closely related to Markov Logic Networks @cite_4 , a formalism originating from Statistical Relational Learning. However, Markov Logic Networks have not been applied to modeling dynamic domains due to its limited expressivity from its logical part.
@cite_4
2119421136 1576159843 1977970897 1585529040
Markov logic is a widely used tool in statistical relational learning, which uses a weighted first-order logic knowledge base to specify a Markov random field (MRF) or a conditional random field (CRF). In many applications, a Markov logic network (MLN) is trained in one domain, but used in a different one. This paper focuses on dynamic Markov logic networks, where the size of the discretized time-domain typically varies between training and testing. It has been previously pointed out that the marginal probabilities of truth assignments to ground atoms can change if one extends or reduces the domains of predicates in an MLN. We show that in addition to this problem, the standard way of unrolling a Markov logic theory into a MRF may result in time-inhomogeneity of the underlying Markov chain. Furthermore, even if these representational problems are not significant for a given domain, we show that the more practical problem of generating samples in a sequential conditional random field for the next slice relying on the samples from the previous slice has high computational cost in the general case, due to the need to estimate a normalization factor for each sample. We propose a new discriminative model, slice normalized dynamic Markov logic networks (SN-DMLN), that suffers from none of these issues. It supports efficient online inference, and can directly model influences between variables within a time slice that do not have a causal direction, in contrast with fully directed models (e.g., DBNs). Experimental results show an improvement in accuracy over previous approaches to online inference in dynamic Markov logic networks. Markov Logic Networks (MLNs) combine Markov networks and first-order logic by attaching weights to first-order formulas and viewing these as templates for features of Markov networks. Learning the structure of MLNs is performed by state-of-the-art methods by maximizing the likelihood of a relational database. This can lead to suboptimal results given prediction tasks. On the other hand better results in prediction problems have been achieved by discriminative learning of MLNs weights given a certain structure. In this paper we propose an algorithm for learning the structure of MLNs discriminatively by maximimizing the conditional likelihood of the query predicates instead of the joint likelihood of all predicates. The algorithm chooses the structures by maximizing conditional likelihood and sets the parameters by maximum likelihood. Experiments in two real-world domains show that the proposed algorithm improves over the state-of-the-art discriminative weight learning algorithm for MLNs in terms of conditional likelihood. We also compare the proposed algorithm with the state-of-the-art generative structure learning algorithm for MLNs and confirm the results in [22] showing that for small datasets the generative algorithm is competitive, while for larger datasets the discriminative algorithm outperfoms the generative one. We propose a simple approach to combining first-order logic and probabilistic graphical models in a single representation. A Markov logic network (MLN) is a first-order knowledge base with a weight attached to each formula (or clause). Together with a set of constants representing objects in the domain, it specifies a ground Markov network containing one feature for each possible grounding of a first-order formula in the KB, with the corresponding weight. Inference in MLNs is performed by MCMC over the minimal subset of the ground network required for answering the query. Weights are efficiently learned from relational databases by iteratively optimizing a pseudo-likelihood measure. Optionally, additional clauses are learned using inductive logic programming techniques. Experiments with a real-world database and knowledge base in a university domain illustrate the promise of this approach. Handling inherent uncertainty and exploiting compositional structure are fundamental to understanding and designing large-scale systems. Statistical relational learning builds on ideas from probability theory and statistics to address uncertainty while incorporating tools from logic, databases and programming languages to represent structure. In Introduction to Statistical Relational Learning, leading researchers in this emerging area of machine learning describe current formalisms, models, and algorithms that enable effective and robust reasoning about richly structured systems and data. The early chapters provide tutorials for material used in later chapters, offering introductions to representation, inference and learning in graphical models, and logic. The book then describes object-oriented approaches, including probabilistic relational models, relational Markov networks, and probabilistic entity-relationship models as well as logic-based formalisms including Bayesian logic programs, Markov logic, and stochastic logic programs. Later chapters discuss such topics as probabilistic models with unknown objects, relational dependency networks, reinforcement learning in relational domains, and information extraction. By presenting a variety of approaches, the book highlights commonalities and clarifies important differences among proposed approaches and, along the way, identifies important representational and algorithmic issues. Numerous applications are provided throughout.Lise Getoor is Assistant Professor in the Department of Computer Science at the University of Maryland. Ben Taskar is Assistant Professor in the Computer and Information Science Department at the University of Pennsylvania.