Related papers: Knowledge and ignorance in Belnap--Dunn logic

Bob has a black box that emits a single pure state qudit which is, from his perspective, uniformly distributed. Alice wishes to give Bob evidence that she has knowledge about the emitted state while giving him little or no information about…

Although large language models (LLMs) excel in knowledge recall and reasoning, their static nature leads to outdated information as the real world evolves or when adapting to domain-specific knowledge, highlighting the need for effective…

In this work, we argue that ignorance can be inherently understood as a hyperintensional notion. When faced with two logically or necessarily equivalent propositions, an agent may be ignorant of one while not of the other. To capture…

Traditional deep neural nets (NNs) have shown the state-of-the-art performance in the task of classification in various applications. However, NNs have not considered any types of uncertainty associated with the class probabilities to…

Epistemic Uncertainty is a measure of the lack of knowledge of a learner which diminishes with more evidence. While existing work focuses on using the variance of the Bayesian posterior due to parameter uncertainty as a measure of epistemic…

Physics-informed neural networks (PINNs) [4, 10] are an approach for solving boundary value problems based on differential equations (PDEs). The key idea of PINNs is to use a neural network to approximate the solution to the PDE and to…

Concept-based explanation methods, such as concept bottleneck models (CBMs), aim to improve the interpretability of machine learning models by linking their decisions to human-understandable concepts, under the critical assumption that such…

Intuitionistic epistemic logic introduces an epistemic operator, which reflects the intended BHK semantics of intuitionism, to intuitionistic logic. The fundamental assumption concerning intuitionistic knowledge and belief is that it is the…

Here, we show that the InfoNCE objective is equivalent to the ELBO in a new class of probabilistic generative model, the recognition parameterised model (RPM). When we learn the optimal prior, the RPM ELBO becomes equal to the mutual…

Current methods for Black-Box NLP interpretability, like LIME or SHAP, are based on altering the text to interpret by removing words and modeling the Black-Box response. In this paper, we outline limitations of this approach when using…

Recent concept-based interpretable models have succeeded in providing meaningful explanations by pre-defined concept sets. However, the dependency on the pre-defined concepts restricts the application because of the limited number of…

Nonmonotonic logics are usually characterized by the presence of some notion of 'conditional' that fails monotonicity. Research on nonmonotonic logics is therefore largely concerned with the defeasibility of argument forms and the…

Information Theory (IT) has been used in Machine Learning (ML) from early days of this field. In the last decade, advances in Deep Neural Networks (DNNs) have led to surprising improvements in many applications of ML. The result has been a…

Recent years witness a growing interest in nonstandard epistemic logics of "knowing whether", "knowing what", "knowing how", and so on. These logics are usually not normal, i.e., the standard axioms and reasoning rules for modal logic may…

The Doomsday argument and anthropic reasoning are two puzzling examples of probabilistic confirmation. In both cases, a lack of knowledge apparently yields surprising conclusions. Since they are formulated within a Bayesian framework, they…

This paper considers the problem of knowledge inference on large-scale imperfect repositories with incomplete coverage by means of embedding entities and relations at the first attempt. We propose IIKE (Imperfect and Incomplete Knowledge…

We present a novel definition of an algorithm and its corresponding algorithm language called CoLweb. The merit of CoLweb [1] is that it makes algorithm design so versatile. That is, it forces us to a high-level, proof-carrying,…

Explainable artificial intelligence and interpretable machine learning are research domains growing in importance. Yet, the underlying concepts remain somewhat elusive and lack generally agreed definitions. While recent inspiration from…

Information bottleneck is an information-theoretic principle of representation learning that aims to learn a maximally compressed representation that preserves as much information about labels as possible. Under this principle, two…

Bayesian Belief Networks (BBNs) are a powerful formalism for reasoning under uncertainty but bear some severe limitations: they require a large amount of information before any reasoning process can start, they have limited contradiction…