Related papers: Bayesian Entailment Hypothesis: How Brains Impleme…

Propositional Typicality Logic (PTL) is a recently proposed logic, obtained by enriching classical propositional logic with a typicality operator capturing the most typical (alias normal or conventional) situations in which a given sentence…

We examine the complexity of inference in Bayesian networks specified by logical languages. We consider representations that range from fragments of propositional logic to function-free first-order logic with equality; in doing so we cover…

Machine learning is the science of discovering statistical dependencies in data, and the use of those dependencies to perform predictions. During the last decade, machine learning has made spectacular progress, surpassing human performance…

Attention-based neural networks have achieved state-of-the-art results on a wide range of tasks. Most such models use deterministic attention while stochastic attention is less explored due to the optimization difficulties or complicated…

We consider the problem of Recognizing Textual Entailment within an Information Retrieval context, where we must simultaneously determine the relevancy as well as degree of entailment for individual pieces of evidence to determine a yes/no…

This note is concerned with a formal analysis of the problem of non-monotonic reasoning in intelligent systems, especially when the uncertainty is taken into account in a quantitative way. A firm connection between logic and probability is…

Predictive coding (PC) is an influential theory of information processing in the brain, providing a biologically plausible alternative to backpropagation. It is motivated in terms of Bayesian inference, as hidden states and parameters are…

Contemporary machine learning methods will try to approach the Bayes error, as it is the lowest possible error any model can achieve. This paper postulates that any decision is composed of not one but two Bayesian decisions and that…

Bayesian networks are directed acyclic graphs representing independence relationships among a set of random variables. A random variable can be regarded as a set of exhaustive and mutually exclusive propositions. We argue that there are…

Monotonicity reasoning is one of the important reasoning skills for any intelligent natural language inference (NLI) model in that it requires the ability to capture the interaction between lexical and syntactic structures. Since no test…

Language models are essentially probability distributions over token sequences. Auto-regressive models generate sentences by iteratively computing and sampling from the distribution of the next token. This iterative sampling introduces…

Learning to reason and carefully explain arguments is central to students' cognitive, mathematical, and computational thinking development. This is particularly challenging in problems under uncertainty and in Bayesian reasoning. With the…

Various AI models are increasingly being considered as part of clinical decision-support tools. However, the trustworthiness of such models is rarely considered. Clinicians are more likely to use a model if they can understand and trust its…

Recent advances in Bayesian probability theory and its application to cognitive science in combination with the development of a new generation of computational tools and methods for probabilistic computation have led to a 'probabilistic…

The intuitive reasoning of physicists in conditions of uncertainty is closer to the Bayesian approach than to the frequentist ideas taught at University and which are considered the reference framework for handling statistical problems. The…

Complex adaptive agents consistently achieve their goals by solving problems that seem to require an understanding of causal information, information pertaining to the causal relationships that exist among elements of combined…

In this paper a conditional logic is defined and studied. This conditional logic, DmBL, is constructed as close as possible to the Bayesian and is unrestricted, that is one is able to use any operator without restriction. A notion of…

Bayesian methods for machine learning have been widely investigated, yielding principled methods for incorporating prior information into inference algorithms. In this survey, we provide an in-depth review of the role of Bayesian methods…

We present a computational model of mathematical reasoning according to which mathematics is a fundamentally stochastic process. That is, on our model, whether or not a given formula is deemed a theorem in some axiomatic system is not a…

We study a regularized variant of the Bayesian Persuasion problem, where the receiver's decision process includes a divergence-based penalty that accounts for deviations from perfect rationality. This modification smooths the underlying…