Related papers: Symbolic Knowledge Extraction using {\L}ukasiewicz…

Issues of safety, explainability, and efficiency are of increasing concern in learning systems deployed with hard and soft constraints. Symbolic Constrained Learning and Knowledge Distillation techniques have shown promising results in this…

Knowledge representation and reasoning in neural networks have been a long-standing endeavor which has attracted much attention recently. The principled integration of reasoning and learning in neural networks is a main objective of the…

A hallmark of human cognition is the ability to continually acquire and distill observations of the world into meaningful, predictive theories. In this paper we present a new mechanism for logical theory acquisition which takes a set of…

In the recent past, there has been a growing interest in Neural-Symbolic Integration frameworks, i.e., hybrid systems that integrate connectionist and symbolic approaches to obtain the best of both worlds. In this work we focus on a…

Inspired by empirical work in neuroscience for Bayesian approaches to brain function, we give a unified probabilistic account of various types of symbolic reasoning from data. We characterise them in terms of formal logic using the…

Neurosymbolic AI combines the interpretability, parsimony, and explicit reasoning of classical symbolic approaches with the statistical learning of data-driven neural approaches. Models and policies that are simultaneously differentiable…

Based on the already known connection between multilayer perceptrons and Lukasiewicz logic with rational coefficients, we take a step forward in analyzing its training process using a three-sorted hybrid modal logic: a multilayer perceptron…

Current high-performance semantic segmentation models are purely data-driven sub-symbolic approaches and blind to the structured nature of the visual world. This is in stark contrast to human cognition which abstracts visual perceptions at…

The multi-valued logic of {\L}ukasiewicz is a substructural logic that has been widely studied and has many interesting properties. It is classical, in the sense that it admits the axiom schema of double negation, [DNE]. However, our…

The recent developments and growing interest in neural-symbolic models has shown that hybrid approaches can offer richer models for Artificial Intelligence. The integration of effective relational learning and reasoning methods is one of…

Although traditional symbolic reasoning methods are highly interpretable, their application in knowledge graph link prediction is limited due to their low computational efficiency. In this paper, we propose a new neural symbolic reasoning…

Most deep neural networks are considered to be black boxes, meaning their output is hard to interpret. In contrast, logical expressions are considered to be more comprehensible since they use symbols that are semantically close to natural…

We introduce neural networks for end-to-end differentiable proving of queries to knowledge bases by operating on dense vector representations of symbols. These neural networks are constructed recursively by taking inspiration from the…

Deep learning methods capable of handling relational data have proliferated over the last years. In contrast to traditional relational learning methods that leverage first-order logic for representing such data, these deep learning methods…

In this paper, our aim is to briefly survey and articulate the logical and philosophical foundations of using (first-order) logic to represent (probabilistic) knowledge in a non-technical fashion. Our motivation is three fold. First, for…

We propose the Neural Logic Machine (NLM), a neural-symbolic architecture for both inductive learning and logic reasoning. NLMs exploit the power of both neural networks---as function approximators, and logic programming---as a symbolic…

A recommendation system assists users in finding items that are relevant to them. Existing recommendation models are primarily based on predicting relationships between users and items and use complex matching models or incorporate…

Knowledge graphs are an expressive and widely used data structure due to their ability to integrate data from different domains in a sensible and machine-readable way. Thus, they can be used to model a variety of systems such as molecules…

Our main contribution is to show that the behaviour of kernels across multiple layers of a convolutional neural network can be approximated using a logic program. The extracted logic programs yield accuracies that correlate with those of…

Numerous neuro-symbolic approaches have recently been proposed typically with the goal of adding symbolic knowledge to the output layer of a neural network. Ideally, such losses maximize the probability that the neural network's predictions…