Related papers: It's Common Knowledge
The Monty Hal problem is an attractive puzzle. It combines simple statement with answers that seem surprising to most audiences. The problem was thoroughly solved over two decades ago. Yet, more recent discussions indicate that the solution…
New numbers, called Guinness numbers, are introduced using certain function of natural argument. Few problems related to these numbers are formulated.
This article deals with theoretical developments in the subject of quantum information and quantum computation, and includes an overview of classical information and some relevant quantum mechanics. The discussion covers topics in quantum…
Negation is a common and important semantic feature in natural language, yet Large Language Models (LLMs) struggle when negation is involved in natural language understanding tasks. Commonsense knowledge, on the other hand, despite being a…
Interpretational questions that arise in the Consistent Histories formulation of quantum mechanics are illustrated by the familiar example of a beam passing through multiple slits.
Entanglement, a puzzle since Einstein's time, has become increasingly crucial with the rise of quantum computation. But what exactly is it? Historically , entanglement can be precisely defined, but only negatively. In this article, we…
It remains an open question whether incorporating external knowledge benefits commonsense reasoning while maintaining the flexibility of pretrained sequence models. To investigate this question, we develop generated knowledge prompting,…
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…
Guo-Niu Han [arXiv:2006.14070 [math.CO]] has introduced a new combinatorial object named standard puzzle. We use digraphs to show the relations between numbers in standard puzzles and propose a skeleton model. By this model, we solve the…
A number of unsolved problems and open questions about the nature and the properties of supernovae are identified and briefly discussed. Some suggestions and directions toward possible solutions are also considered.
Hardin introduced the notorious concept of "tragedy of the commons". Worrying about the consequences of human overpopulation on the planet, he discussed "hard problems": problems with no technical solutions, that can only be addressed by…
It gives some new forms of General Neron Desingularization and new applications.
Uncertainty enters into human reasoning and inference in at least two ways. It is reasonable to suppose that there will be roles for these distinct uses of uncertainty also in automated reasoning.
Taking a new approach towards analyzing the Collatz Problem, or, 3x+1 conjecture. Introducing some new functions, the Collatz-2 and Collatz-3 sequences, as well as deducing results related to Collatz-2 and Collatz-3 sequences.
Knowledge structures called Concept Clustering Knowledge Graphs (CCKGs) are introduced along with a process for their construction from a machine readable dictionary. CCKGs contain multiple concepts interrelated through multiple semantic…
We treat interpolation for various logics.
We investigate how knowledge percolates and clusters in a given knowledge space. We introduce a simple model of knowledge organization in which each contribution spans a certain number of items. If this contribution overlaps with others…
This essay considers ways that recent uses of computers in mathematics challenge contemporary views on the nature of mathematical understanding. It also puts these challenges in a historical perspective and offers speculation as to a…
It is rare to succeed in getting mathematics into ordinary conversation without meeting all kinds of reservations. In order to raise public awareness of mathematics effectively, it is necessary to modify such attitudes. In this paper, we…
An introductory guide to mathematical cosmology is given focusing on the issue of the genericity of various important results which have been obtained during the last thirty or so years. Some of the unsolved problems along with certain new…