Related papers: Logic Tensor Networks: Deep Learning and Logical R…

A logic program is an executable specification. For example, merge sort in pure Prolog is a logical formula, yet shows creditable performance on long linked lists. But such executable specifications are a compromise: the logic is distorted…

One approach to explaining the hierarchical levels of understanding within a machine learning model is the symbolic method of inductive logic programming (ILP), which is data efficient and capable of learning first-order logic rules that…

A tensor network is a type of decomposition used to express and approximate large arrays of data. A given data-set, quantum state or higher dimensional multi-linear map is factored and approximated by a composition of smaller multi-linear…

This paper presents LEXR, a framework for explaining the decision making of recurrent neural networks (RNNs) using a formal description language called Linear Temporal Logic (LTL). LTL is the de facto standard for the specification of…

Today, the dominant paradigm for training neural networks involves minimizing task loss on a large dataset. Using world knowledge to inform a model, and yet retain the ability to perform end-to-end training remains an open question. In this…

We provide a denotational semantics for first-order logic that captures the two-level view of the computation process typical for constraint programming. At one level we have the usual program execution. At the other level an automatic…

We present a neurosymbolic approach, i.e., combining symbolic and subsymbolic artificial intelligence, to validating offer documents in regulated public institutions. We employ a language model to extract information and then aggregate with…

Probabilistic logical models are a core component of neurosymbolic AI and are important in their own right for tasks that require high explainability. Unlike neural networks, logical theories that underlie the model are often handcrafted…

We propose a novel way to incorporate expert knowledge into the training of deep neural networks. Many approaches encode domain constraints directly into the network architecture, requiring non-trivial or domain-specific engineering. In…

Deep neural networks are widely used for classification. These deep models often suffer from a lack of interpretability -- they are particularly difficult to understand because of their non-linear nature. As a result, neural networks are…

The field of statistical relational learning aims at unifying logic and probability to reason and learn from data. Perhaps the most successful paradigm in the field is probabilistic logic programming: the enabling of stochastic primitives…

We solve high-dimensional steady-state Fokker-Planck equations on the whole space by applying tensor neural networks. The tensor networks are a linear combination of tensor products of one-dimensional feedforward networks or a linear…

In this paper, we introduce Interval Real Logic (IRL), a two-sorted logic that interprets knowledge such as sequential properties (traces) and event properties using sequences of real-featured data. We interpret connectives using fuzzy…

Situated as a language between computer science, quantum physics and mathematics, tensor network theory has steadily grown in popularity and can now be found in applications ranging across the entire field of quantum information processing.…

We introduce DeepProbLog, a neural probabilistic logic programming language that incorporates deep learning by means of neural predicates. We show how existing inference and learning techniques of the underlying probabilistic logic…

Deep learning models with convolutional and recurrent networks are now ubiquitous and analyze massive amounts of audio, image, video, text and graph data, with applications in automatic translation, speech-to-text, scene understanding,…

Logical reasoning of text requires understanding critical logical information in the text and performing inference over them. Large-scale pre-trained models for logical reasoning mainly focus on word-level semantics of text while struggling…

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…

Despite the extensive investment and impressive recent progress at reasoning by similarity, deep learning continues to struggle with more complex forms of reasoning such as non-monotonic and commonsense reasoning. Non-monotonicity is a…

Logical formalisms provide a natural and concise means for specifying and reasoning about preferences. In this paper, we propose lexicographic logic, an extension of classical propositional logic that can express a variety of preferences,…