This paper solves the task of knowledge base completion i.e. filling the missing relations between two entities by combining Statistical Relational Model like Markov Logic, and knowledge graph embedding method like TransE. Authors define a set of rules to be used in MLNs and then define a joint probability distribution over the observed and hidden triplets. Similarly, they define a joint probability distribution using KGE approaches (specifically they chose transE model). Then they employ the variational EM algorithm to learn the MLN weights and finally predicting the probabilities of hidden triplets. Originality: I really liked the paper, and enjoyed thoroughly reading it.

We consider the problem of learning rules from natural language text sources. These sources, such as news articles and web texts, are created by a writer to communicate information to a reader, where the writer and reader share substantial domain knowledge. Consequently, the texts tend to be concise and mention the minimum information necessary for the reader to draw the correct conclusions. We study the problem of learning domain knowledge from such concise texts, which is an instance of the general problem of learning in the presence of missing data. However, unlike standard approaches to missing data, in this setting we know that facts are more likely to be missing from the text in cases where the reader can infer them from the facts that are mentioned combined with the domain knowledge.

Neural network performance has made great strides in recent years by incorporating key assumptions, often referred to as inductive biases, about data domains into specialized model structures. The designs of popular neural network architectures such as recurrent neural networks, convolutional neural networks, graph neural networks, and transformers all incorporate aspects of their respective task-specific domains into the operations, weight sharing, and connections of their underlying network structure [1, 3, 4, 9, 12]. That specialization, has, in turn, yielded improved efficiency and performance over the more general, fully connected design. Note, however, when implemented, these neural networks tend to be treated as entirely separate architectures, with no explicit connections between them, despite their similar underlying assumptions. Not only does this practice obscures some of the core theoretical similarities between these models, but it can also make modifying the architecture cumbersome when any of those original assumptions about the task domain change even slightly. There exist several well-established methods for describing and reasoning from logical knowledge bases that could trivially describe both the assumptions made on a task's domain and the graphical structure of the neural network itself. Nonetheless, simply using deterministic logic on its own to define that structure, through any given logical programming language, does not immediately align with the constrained structure of the neural network and the uncertainty present in said network's predictions.

We introduce the concept of weighted rules under the stable model semantics following the log-linear models of Markov Logic. This provides versatile methods to overcome the deterministic nature of the stable model semantics, such as resolving inconsistencies in answer set programs, ranking stable models, associating probability to stable models, and applying statistical inference to computing weighted stable models. We also present formal comparisons with related formalisms, such as answer set programs, Markov Logic, ProbLog, and P-log.

For many years, the two dominant paradigms in artificial intelligence (AI) have been logical AI and statistical AI. Logical AI uses first-order logic and related representations to capture complex relationships and knowledge about the world. However, logic-based approaches are often too brittle to handle the uncertainty and noise present in many applications. Statistical AI uses probabilistic representations such as probabilistic graphical models to capture uncertainty. However, graphical models only represent distributions over propositional universes and must be customized to handle relational domains. As a result, expressing complex concepts and relationships in graphical models is often difficult and labor-intensive.

LPMLN is a probabilistic extension of answer set programs with the weight scheme derived from that of Markov Logic. Previous work has shown how inference in LPMLN can be achieved. In this paper, we present the concept of weight learning in LPMLN and learning algorithms for LPMLN derived from those for Markov Logic. We also present a prototype implementation that uses answer set solvers for learning as well as some example domains that illustrate distinct features of LPMLN learning. Learning in LPMLN is in accordance with the stable model semantics, thereby it learns parameters for probabilistic extensions of knowledge-rich domains where answer set programming has shown to be useful but limited to the deterministic case, such as reachability analysis and reasoning about actions in dynamic domains. We also apply the method to learn the parameters for probabilistic abductive reasoning about actions.

Advances in machine learning, including deep learning, have propelled artificial intelligence (AI) into the public conscience and forced executives to create new business plans based on data. However, the scarcity of highly trained data scientists has stymied many machine learning implementations, potentially blocking future AI development. Now a group of academics and technologist say the emerging fields of Markov Logic and probabilistic programming could lower the bar for implementing machine learning. Markov Logic is a language first described in by two professors in the University of Washington's Department of Computer Science and Engineering, Pedro Domingos and Matthew Richardson, in their seminal 2006 paper "Markov Logic Networks." The work is based on mathematical discoveries made by Andrey Markov Jr., the Soviet mathematician who died in 1979 (his father, who had the same name, is associated with a related field, dubbed Markov chains).

We argue that second-order Markov logic is ideally suited for this purpose and propose an approach based on it. Our algorithm discovers structural regularities in the source domain in the form of Markov logic formulas with predicate variables and instantiates these formulas with predicates from the target domain. Our approach has successfully transferred learned knowledge among molecular biology, web, and social network domains. For example, Wall Street firms often hire physicists to solve finance problems. Even though these two domains have superficially nothing in common, training as a physicist provides knowledge and skills that are highly applicable in finance (for example, solving differential equations and performing Monte Carlo simulations).

We introduce the concept of weighted rules under the stable model semantics following the log-linear models of Markov Logic. This provides versatile methods to overcome the deterministic nature of the stable model semantics, such as resolving inconsistencies in answer set programs, ranking stable models, associating probability to stable models, and applying statistical inference to computing weighted stable models. We also present formal comparisons with related formalisms, such as answer set programs, Markov Logic, ProbLog, and P-log.

Markov Logic Networks (MLNs) use a few weighted first-order logic formulas to represent large probabilistic graphical models and are ideally suited for representing both relational and probabilistic knowledge in a wide variety of application domains such as, NLP, computer vision, and robotics. However, inference in them is hard because the graphical models can be extremely large, having millions of variables and features (potentials). Therefore, several lifted inference algorithms that exploit relational structure and operate at the compact first-order level, have been developed in recent years. However, the focus of much of existing research on lifted inference is on marginal inference while algorithms for MAP and marginal MAP inference are far less advanced. The aim of the proposed thesis is to fill this void, by developing next generation inference algorithms for MAP and marginal MAP inference.