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Qualitative and quantitative approaches to reasoning about uncertainty can lead to different logical systems for formalizing such reasoning, even when the language for expressing uncertainty is the same. In the case of reasoning about…

Recent efforts to improve the reasoning abilities of Large Language Models (LLMs) have focused on integrating formal logic solvers within neurosymbolic frameworks. A key challenge is that formal solvers lack commonsense world knowledge,…

In this paper, we propose a new deep learning approach, called neural association model (NAM), for probabilistic reasoning in artificial intelligence. We propose to use neural networks to model association between any two events in a…

In recent years, reinforcement learning (RL) has emerged as a popular approach for solving sequence-based tasks in machine learning. However, finding suitable alternatives to RL remains an exciting and innovative research area. One such…

With the rise of increasingly powerful and user-facing NLP systems, there is growing interest in assessing whether they have a good representation of uncertainty by evaluating the quality of their predictive distribution over outcomes. We…

This paper investigates the use of probabilistic neural networks (PNNs) to model aleatoric uncertainty, which refers to the inherent variability in the input-output relationships of a system, often characterized by unequal variance or…

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…

We present a propositional logic to reason about the uncertainty of events, where the uncertainty is modeled by a set of probability measures assigning an interval of probability to each event. We give a sound and complete axiomatization…

Uncertain information is being taken into account in an increasing number of application fields. In the meantime, abduction has been proved a powerful tool for handling hypothetical reasoning and incomplete knowledge. Probabilistic logical…

Advances in the general capabilities of large language models (LLMs) have led to their use for information retrieval, and as components in automated decision systems. A faithful representation of probabilistic reasoning in these models may…

Bayesian Neural Networks (BNNs) place priors over the parameters in a neural network. Inference in BNNs, however, is difficult; all inference methods for BNNs are approximate. In this work, we empirically compare the quality of predictive…

Uncertainty estimation (UE) of generative large language models (LLMs) is crucial for evaluating the reliability of generated sequences. A significant subset of UE methods utilize token probabilities to assess uncertainty, aggregating…

Despite widespread success in language understanding and generation, large language models (LLMs) exhibit unclear and often inconsistent behavior when faced with tasks that require probabilistic reasoning. In this work, we present the first…

Recent empirical work has shown that human children are adept at learning and reasoning with probabilities. Here, we model a recent experiment investigating the development of school-age children's non-symbolic probability reasoning ability…

Increasingly high-stakes decisions are made using neural networks in order to make predictions. Specifically, meteorologists and hedge funds apply these techniques to time series data. When it comes to prediction, there are certain…

We present a propositional logic %which can be used to reason about the uncertainty of events, where the uncertainty is modeled by a set of probability measures assigning an interval of probability to each event. We give a sound and…

Providing explanations for the outputs of artificial neural networks (ANNs) is crucial in many contexts, such as critical systems, data protection laws and handling adversarial examples. Logic-based methods can offer explanations with…

Mechanisms for the automation of uncertainty are required for expert systems. Sometimes these mechanisms need to obey the properties of probabilistic reasoning. A purely numeric mechanism, like those proposed so far, cannot provide a…

Large Language Models (LLMs) are increasingly used as powerful tools for several high-stakes natural language processing (NLP) applications. Recent prompting works claim to elicit intermediate reasoning steps and key tokens that serve as…

The relationship between communicated language and intended meaning is often probabilistic and sensitive to context. Numerous strategies attempt to estimate such a mapping, often leveraging recursive Bayesian models of communication. In…