Related papers: The Topological Structure of Question Theory
The classifying topos of a geometric theory is a topos such that geometric morphisms into it correspond to models of that theory. We study classifying toposes for different infinitary logics: first-order, sub-first-order (i.e. geometric…
This article belongs to a subject, Directed Algebraic Topology, whose general aim is including non-reversible processes in the range of topology and algebraic topology. Here, as a further step, we also want to cover "critical processes",…
Common research tasks ask students to identify a correct answer and justify their answer choice. We propose expanding the array of research tasks to access different knowledge that students might have. By asking students to discuss answers…
Scholastic trivia competitions test knowledge and intelligence through mastery of question answering. Modern question answering benchmarks are one variant of the Turing test. Specifically, answering a set of questions as well as a human is…
In this paper we study the logical foundations of automated inductive theorem proving. To that aim we first develop a theoretical model that is centered around the difficulty of finding induction axioms which are sufficient for proving a…
Interest in the field of Explainable Artificial Intelligence has been growing for decades and has accelerated recently. As Artificial Intelligence models have become more complex, and often more opaque, with the incorporation of complex…
The paper has a form of a survey and consists of three parts. It is focused on the relationship between the many-sorted theory, which leads to logical geometry and one-sorted theory, which is based on the important model-theoretic concepts.…
The goal of this paper is to summarise the first steps in developing a fundamentally new way of constructing theories of physics. The motivation comes from a desire to address certain deep issues that arise when contemplating quantum…
Most learners fail to develop deep text comprehension when reading textbooks passively. Posing questions about what learners have read is a well-established way of fostering their text comprehension. However, many textbooks lack…
A central quest in explainable AI relates to understanding the decisions made by (learned) classifiers. There are three dimensions of this understanding that have been receiving significant attention in recent years. The first dimension…
We introduce a new kind of Information Theory. From a finite number of local, noisy comparisons, we want to design a robust filter such that the outcome is a high ranking number, Both analytical and numerical results are encouraging and we…
Logical theories in the form of ontologies and similar artefacts in computing and IT are used for structuring, annotating, and querying data, among others, and therewith influence data analytics regarding what is fed into the algorithms.…
Trustworthy language models should abstain from answering questions when they do not know the answer. However, the answer to a question can be unknown for a variety of reasons. Prior research has focused on the case in which the question is…
The ability to ask questions is important in both human and machine intelligence. Learning to ask questions helps knowledge acquisition, improves question-answering and machine reading comprehension tasks, and helps a chatbot to keep the…
This book is expository and is in Russian. It is shown how in the course of solution of interesting geometric problems (close to applications) naturally appear main notions of algebraic topology (homology groups, obstructions and…
Homotopy Type Theory is a new field of mathematics based on the surprising and elegant correspondence between Martin-Lofs constructive type theory and abstract homotopy theory. We have a powerful interplay between these disciplines - we can…
We present a theory of information expressed solely in terms of which transformations of physical systems are possible and which are impossible - i.e. in constructor-theoretic terms. Although it includes conjectured laws of physics that are…
Theory based AI research has had a hard time recently and the aim here is to propose a model of what LLMs are actually doing when they impress us with their language skills. The model integrates three established theories of human…
We introduce the notion of a logical model category which is a Quillen model category satisfying some additional conditions. Those conditions provide enough expressive power that one can soundly interpret dependent products and sums in it.…
Constructivists (and intuitionists in general) asked what kind of mental construction is needed to convince ourselves (and others) that some mathematical statement is true. This question has a much more practical (and even cynical)…