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Data originating from the Web, sensor readings and social media result in increasingly huge datasets. The so called Big Data comes with new scientific and technological challenges while creating new opportunities, hence the increasing…

In real-world applications, knowledge bases consisting of all the information at hand for a specific domain, along with the current state of affairs, are bound to contain contradictory data coming from different sources, as well as data…

In many probabilistic first-order representation systems, inference is performed by "grounding"---i.e., mapping it to a propositional representation, and then performing propositional inference. With a large database of facts, groundings…

Knowledge graph (KG) reasoning is becoming increasingly popular in both academia and industry. Conventional KG reasoning based on symbolic logic is deterministic, with reasoning results being explainable, while modern embedding-based…

We present a method for dynamically generating Bayesian networks from knowledge bases consisting of first-order probability logic sentences. We present a subset of probability logic sufficient for representing the class of Bayesian networks…

The paradigm of Tabled Logic Programming (TLP) is now supported by a number of Prolog systems, including XSB, YAP Prolog, B-Prolog, Mercury, ALS, and Ciao. The reasons for this are partly theoretical: tabling ensures termination and optimal…

Neural networks have been able to achieve groundbreaking accuracy at tasks conventionally considered only doable by humans. Using stochastic gradient descent, optimization in many dimensions is made possible, albeit at a relatively high…

Multi-hop logical reasoning over knowledge graph (KG) plays a fundamental role in many artificial intelligence tasks. Recent complex query embedding (CQE) methods for reasoning focus on static KGs, while temporal knowledge graphs (TKGs)…

While there are a plethora of methods for link prediction in knowledge graphs, state-of-the-art approaches are often black box, obfuscating model reasoning and thereby limiting the ability of users to make informed decisions about model…

In the rapidly evolving AI era with large language models (LLMs) at the core, making LLMs more trustworthy and efficient, especially in output generation (inference), has gained significant attention. This is to reduce plausible but faulty…

Tensor Network (TN) decompositions have emerged as an indispensable tool in Big Data analytics owing to their ability to provide compact low-rank representations, thus alleviating the ``Curse of Dimensionality'' inherent in handling…

The large size and fast growth of data repositories, such as data lakes, has spurred the need for data discovery to help analysts find related data. The problem has become challenging as (i) a user typically does not know what datasets…

Differentiable logics are a family of quantitative logics originated in the machine learning literature. Because of their origin, differentiable logics often come equipped with analytic properties that guarantee that they are…

Probabilistic independence is a useful concept for describing the result of random sampling---a basic operation in all probabilistic languages---and for reasoning about groups of random variables. Nevertheless, existing verification methods…

Clustering is a fundamental learning task widely used as a first step in data analysis. For example, biologists use cluster assignments to analyze genome sequences, medical records, or images. Since downstream analysis is typically…

Language models are trained on large volumes of text, and as a result their parameters might contain a significant body of factual knowledge. Any downstream task performed by these models implicitly builds on these facts, and thus it is…

Language models generate reasoning sequentially, preventing them from decoupling irrelevant exploration paths during search. We introduce Tree-Structured Language Modeling (TSLM), which uses special tokens to encode branching structure,…

There are significant benefits to serve deep learning models from relational databases. First, features extracted from databases do not need to be transferred to any decoupled deep learning systems for inferences, and thus the system…

We present a mechanism for constructing graphical models, specifically Bayesian networks, from a knowledge base of general probabilistic information. The unique feature of our approach is that it uses a powerful first-order probabilistic…

Parsing natural language questions into executable logical forms is a useful and interpretable way to perform question answering on structured data such as knowledge bases (KB) or databases (DB). However, existing approaches on semantic…