Related papers: Truth and Knowledge
'Fake News' continues to undermine trust in modern journalism and politics. Despite continued efforts to study fake news, results have been conflicting. Previous attempts to analyse and combat fake news have largely focused on…
In this paper we give a self contained introduction to the conceptional and mathematical foundations of quantum information theory. In the first part we introduce the basic notions like entanglement, channels, teleportation etc. and their…
This article contains ideas and their elaboration for quantifiers, which appeared after checking in practice the experimental language of the formal knowledge representation YAFOLL [1]: - looking at for_all and exists quantifiers as…
We have a lot of relation to the encoding and the Theory of Information, when considering thinking. This is a natural process and, at once, the complex thing we investigate. This always was a challenge - to understand how our mind works,…
Human knowledge is subject to uncertainties, imprecision, incompleteness and inconsistencies. Moreover, the meaning of many everyday terms is dependent on the context. That poses a huge challenge for the Semantic Web. This paper introduces…
We provide a formal introduction into the classic theorems of general topology and its axiomatic foundations in set theory. In this second part we introduce the fundamental concepts of topological spaces, convergence, and continuity, as…
Essentially being an extended abstract of the author's 1998 PhD thesis, this paper introduces an extension of the language of linear logic with a semantics which treats sentences as tasks rather than true/false statements. A resource is…
This is a broad and in places unconventional overview of the strengths and shortcomings of our standard models of fundamental physics and of cosmology. The emphasis is on ideas that have accessible experimental consequences. It becomes…
When reasoning in description, modal or temporal logics it is often useful to consider axioms representing universal truths in the domain of discourse. Reasoning with respect to an arbitrary set of axioms is hard, even for relatively…
Length generalization (LG) is a challenging problem in learning to reason. It refers to the phenomenon that when trained on reasoning problems of smaller lengths or sizes, the resulting model struggles with problems of larger sizes or…
Tarski's semantic definition of truth is the composition of its extensional and intensional aspects. Abstract satisfaction, the core of the semantic definition of truth, is the basis for the theory of institutions (Goguen and Burstall). The…
This paper avers that science is not demarcated from other disciplines by a specific unique methodology, but by its specific scientific rationality and rational grounds. In this context, the notion and structure of scientific reason are…
This paper proposes an approach to framing and answering fundamental questions about consciousness. It argues that many of the more theoretical debates about consciousness, such as debates about "when does it begin?", are misplaced and…
This paper is motivated by the questions of how to give the concept of probability an adequate real-world meaning, and how to explain a certain type of phenomenon that can be found, for instance, in Ellsberg's paradox. It attempts to answer…
Large Language Models (LLMs) store an extensive amount of factual knowledge obtained from vast collections of text. To effectively utilize these models for downstream tasks, it is crucial to have reliable methods for measuring their…
We formalize the general principle of significance with respect to binary relations which is a universal tool for description and analysis of various situations in and apart from mathematics. We derive the basic properties and focus on a…
Despite recent advances in abstractive summarization, current summarization systems still suffer from content hallucinations where models generate text that is either irrelevant or contradictory to the source document. However, prior work…
Information-theoretic measures such as relative entropy and correlation are extremely useful when modeling or analyzing the interaction of probabilistic systems. We survey the quantum generalization of 5 such measures and point out some of…
A number of topics in analysis are discussed, with emphasis on basic principles. There is some overlap with "Elements of linear and real analysis" (arXiv:math/0108030), with numerous changes in content and presentation since then.
Although the notion of a concept as a collection of objects sharing certain properties, and the notion of a conceptual hierarchy are fundamental to both Formal Concept Analysis and Description Logics, the ways concepts are described and…