Related papers: Reconstruct the Logical Network from the Transitio…

Traditional neural networks have an impressive classification performance, but what they learn cannot be inspected, verified or extracted. Neural Logic Networks on the other hand have an interpretable structure that enables them to learn a…

Consider a binary classification problem solved using a feed-forward artificial neural network (ANN). Let the ANN be composed of a ReLU layer and several linear layers (convolution, sum-pooling, or fully connected). We assume the network…

We propose $\mathcal{T}$ruth $\mathcal{T}$able net ($\mathcal{TT}$net), a novel Convolutional Neural Network (CNN) architecture that addresses, by design, the open challenges of interpretability, formal verification, and logic gate…

The notion of Boolean logic backpropagation was introduced to build neural networks with weights and activations being Boolean numbers. Most of computations can be done with Boolean logic instead of real arithmetic, both during training and…

Large Language Models (LLMs) face significant accuracy degradation due to insufficient reasoning ability when dealing with complex and abstract tasks. Thought structures such as Chain of Thought (CoT) and Tree of Thought (ToT) focus on…

While neural networks are good at learning unspecified functions from training samples, they cannot be directly implemented in hardware and are often not interpretable or formally verifiable. On the other hand, logic circuits are…

Machine reading comprehension (MRC) poses new challenges over logical reasoning, which aims to understand the implicit logical relations entailed in the given contexts and perform inference over them. Due to the complexity of logic, logical…

To solve more complex things, computer systems becomes more and more complex. It becomes harder to be handled manually for various conditions and unknown new conditions in advance. This situation urgently requires the development of…

As knowledge and semantics on the web grow increasingly complex, enhancing Large Language Models (LLMs)' comprehension and reasoning capabilities has become particularly important. Chain-of-Thought (CoT) prompting has been shown to enhance…

Recent machine reading comprehension datasets such as ReClor and LogiQA require performing logical reasoning over text. Conventional neural models are insufficient for logical reasoning, while symbolic reasoners cannot directly apply to…

Based on the property that solving the system of linear matrix equations via the column space and the row space projections boils down to an approximation in the least squares error sense, a formulation for learning the weight matrices of…

We propose a novel learning paradigm for Deep Neural Networks (DNN) by using Boolean logic algebra. We first present the basic differentiable operators of a Boolean system such as conjunction, disjunction and exclusive-OR and show how these…

This paper develops a proof-theoretic framework for abstract interpretation by systematically associating logical systems with finite abstractions. Building on earlier work on the internal logics of abstractions, we propose a general…

Linear implication can represent state transitions, but real transition systems operate under temporal, stochastic or probabilistic constraints that are not directly representable in ordinary linear logic. We propose a general modal…

Despite their great success in recent years, deep neural networks (DNN) are mainly black boxes where the results obtained by running through the network are difficult to understand and interpret. Compared to e.g. decision trees or bayesian…

A detailed exposition of foundations of a logic-algebraic model for reasoning with knowledge bases specified by propositional (Boolean) logic is presented. The model is conceived from the logical translation of usual derivatives on…

There is growing excitement about building software verifiers, synthesizers, and other Automated Reasoning (AR) tools by combining traditional symbolic algorithms and Large Language Models (LLMs). Unfortunately, the current practice for…

With a view to bridging the gap between deep learning and symbolic AI, we present a novel end-to-end neural network architecture that learns to form propositional representations with an explicitly relational structure from raw pixel data.…

In the article, we discuss the architecture of the polynomial neural network that corresponds to the matrix representation of Lie transform. The matrix form of Lie transform is an approximation of the general solution of the nonlinear…

Machine learning-based methods have achieved successful applications in machinery fault diagnosis. However, the main limitation that exists for these methods is that they operate as a black box and are generally not interpretable. This…