Related papers: TensorLog: A Differentiable Deductive Database

We present Generative Logic (GL), a deterministic architecture that starts from user-supplied axiomatic definitions written in a minimalist Mathematical Programming Language (MPL) and systematically explores a configurable region of their…

Many AI applications rely on knowledge about a relevant real-world domain that is encoded by means of some logical knowledge base (KB). The most essential benefit of logical KBs is the opportunity to perform automatic reasoning to derive…

We propose a framework for modeling uncertainty where both belief and doubt can be given independent, first-class status. We adopt probability theory as the mathematical formalism for manipulating uncertainty. An agent can express the…

The vast quantity of data generated and captured every day has led to a pressing need for tools and processes to organize, analyze and interrelate this data. Automated reasoning and optimization tools with inherent support for data could…

Checklists have been widely recognized as effective tools for completing complex tasks in a systematic manner. Although originally intended for use in procedural tasks, their interpretability and ease of use have led to their adoption for…

State-of-the-art inference approaches in probabilistic logic programming typically start by computing the relevant ground program with respect to the queries of interest, and then use this program for probabilistic inference using knowledge…

Consider a Bayesian inference problem where a variable of interest does not take values in a Euclidean space. These "non-standard" data structures are in reality fairly common. They are frequently used in problems involving latent discrete…

A major reason behind the success of probability calculus is that it possesses a number of valuable tools, which are based on the notion of probabilistic independence. In this paper, I identify a notion of logical independence that makes…

We consider belief propagation (BP) as an efficient and scalable tool for state estimation and optimization problems in supply networks such as power grids. BP algorithms make use of factor graph representations, whose assignment to the…

Deductive and abductive reasoning are two critical paradigms for analyzing knowledge graphs, enabling applications from financial query answering to scientific discovery. Deductive reasoning on knowledge graphs usually involves retrieving…

Formulating and answering logical queries is a standard communication interface for knowledge graphs (KGs). Alleviating the notorious incompleteness of real-world KGs, neural methods achieved impressive results in link prediction and…

There is an increasing interest in scaling tensor network methods through belief propagation (BP), as well as increasing the accuracy of BP through tensor network methods. We develop a unification framework that takes an arbitrary graphical…

Knowledge bases (KB), both automatically and manually constructed, are often incomplete --- many valid facts can be inferred from the KB by synthesizing existing information. A popular approach to KB completion is to infer new relations by…

The increasing demand for deep learning-based foundation models has highlighted the importance of efficient data retrieval mechanisms. Neural graph databases (NGDBs) offer a compelling solution, leveraging neural spaces to store and query…

We describe a representation and a set of inference methods that combine logic programming techniques with probabilistic network representations for uncertainty (influence diagrams). The techniques emphasize the dynamic construction and…

Probabilistic inference is a fundamental task in modern machine learning. Recent advances in tensor network (TN) contraction algorithms have enabled the development of better exact inference methods. However, many common inference tasks in…

Knowledge graphs (KG) have become increasingly important to endow modern recommender systems with the ability to generate traceable reasoning paths to explain the recommendation process. However, prior research rarely considers the…

The knowledge base paradigm aims to express domain knowledge in a rich formal language, and to use this domain knowledge as a knowledge base to solve various problems and tasks that arise in the domain by applying multiple forms of…

Bayesian network classifiers provide a feasible solution to tabular data classification, with a number of merits like high time and memory efficiency, and great explainability. However, due to the parameter explosion and data sparsity…

Abductive reasoning is the process of making educated guesses to provide explanations for observations. Although many applications require the use of knowledge for explanations, the utilization of abductive reasoning in conjunction with…