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Starting with a likelihood or preference order on worlds, we extend it to a likelihood ordering on sets of worlds in a natural way, and examine the resulting logic. Lewis (1973) earlier considered such a notion of relative likelihood in the…

Real-world data often follows a long-tailed distribution, which makes the performance of existing classification algorithms degrade heavily. A key issue is that samples in tail categories fail to depict their intra-class diversity. Humans…

We consider the problem of learning generalized first-order representations of concepts from a single example. To address this challenging problem, we augment an inductive logic programming learner with two novel algorithmic contributions.…

The widespread usage of latent language representations via pre-trained language models (LMs) suggests that they are a promising source of structured knowledge. However, existing methods focus only on a single object per subject-relation…

Large language models (LLMs) have achieved remarkable performance in generating human-like text and solving reasoning tasks of moderate complexity, such as question-answering and mathematical problem-solving. However, their capabilities in…

We develop a system for solving logical deduction one-dimensional ordering problems by transforming natural language premises and candidate statements into first-order logic. Building on Heim and Kratzer's syntax-based compositional…

While Pre-trained Language Models (PLMs) internalize a great amount of world knowledge, they have been shown incapable of recalling these knowledge to solve tasks requiring complex & multi-step reasoning. Similar to how humans develop a…

We introduce DeepPSL a variant of probabilistic soft logic (PSL) to produce an end-to-end trainable system that integrates reasoning and perception. PSL represents first-order logic in terms of a convex graphical model -- hinge-loss Markov…

Intelligent systems based on first-order logic on the one hand, and on artificial neural networks (also called connectionist systems) on the other, differ substantially. It would be very desirable to combine the robust neural networking…

In this paper, we study the sampling problem for first-order logic proposed recently by Wang et al. -- how to efficiently sample a model of a given first-order sentence on a finite domain? We extend their result for the…

We propose a novel framework seamlessly providing key properties of both neural nets (learning) and symbolic logic (knowledge and reasoning). Every neuron has a meaning as a component of a formula in a weighted real-valued logic, yielding a…

The integration of reasoning, learning, and decision-making is key to build more general artificial intelligence systems. As a step in this direction, we propose a novel neural-logic architecture, called differentiable logic machine (DLM),…

Reinforcement Learning (RL) can enable agents to learn complex tasks. However, it is difficult to interpret the knowledge and reuse it across tasks. Inductive biases can address such issues by explicitly providing generic yet useful…

Many latent (factorized) models have been proposed for recommendation tasks like collaborative filtering and for ranking tasks like document or image retrieval and annotation. Common to all those methods is that during inference the items…

Large Language Models (LLMs) have demonstrated strong performance in handling complex tasks requiring both extensive knowledge and reasoning abilities. However, the existing LLM inference pipeline operates as an opaque process without…

We investigate here concept learning from incomplete examples. Our first purpose is to discuss to what extent logical learning settings have to be modified in order to cope with data incompleteness. More precisely we are interested in…

Recent research has highlighted that Large Language Models (LLMs), even when trained to generate extended long reasoning steps, still face significant challenges on hard reasoning problems. However, much of the existing literature relies on…

Mechanistic models with differential equations are a key component of scientific applications of machine learning. Inference in such models is usually computationally demanding, because it involves repeatedly solving the differential…

Statistical learning and logical reasoning are two major fields of AI expected to be unified for human-like machine intelligence. Most existing work considers how to combine existing logical and statistical systems. However, there is no…

Background & Objectives: In the last decade, Machine learning research has grown rapidly, but large models are reaching their soft limits demonstrating diminishing returns and still lack solid reasoning abilities. These limits could be…