Related papers: It's Common Knowledge
This paper is an overview and survey of work on the 3x+1 problem, also called the Collatz problem, and generalizations of it. It gives a history of the problem. It addresses two questions: (1) What can mathematics currently say about this…
Existing commonsense knowledge bases often organize tuples in an isolated manner, which is deficient for commonsense conversational models to plan the next steps. To fill the gap, we curate a large-scale multi-turn human-written…
A sketch of some of the fundamental notions related to the nature of knowledge is offered, with special focus on the role of mathematics and my own opinions. No single idea exposed here is entirely original; indeed, this topic has been…
Reasoning about knowledge seems to play a fundamental role in distributed systems. Indeed, such reasoning is a central part of the informal intuitive arguments used in the design of distributed protocols. Communication in a distributed…
I use an instrumental approach to investigate some commonly made claims about interpretations of quantum mechanics, especially those that pertain questions of locality. The here presented investigation builds on a recently proposed taxonomy…
In this short review we study the state of the art of the great problems in cosmology and their interrelationships. The reconciliation of these problems passes undoubtedly through the idea of a quantum universe.
The Frankl conjecture (called also union-closed sets conjecture) is one of the famous unsolved conjectures in combinatorics of finite sets. In this short note, we introduce and to some extent justify some variants of the Frankl conjecture.
Commonsense knowledge is essential for advancing natural language processing (NLP) by enabling models to engage in human-like reasoning, which requires a deeper understanding of context and often involves making inferences based on implicit…
We introduce more generalizations of BCI, BCK and of Hilbert algebras, with proper examples, and show the hierarchies existing between all these algebras, old and new ones. Namely, we found thirty one new generalizations of BCI and BCK…
Although the amount of knowledge that the humans possess has been gradually increasing, we still do not know the procedure and conditions that lead to the creation of new knowledge. An understanding of the modus operandi for the creation of…
Several new applications of Katona's circle are given.
In problem solving, understanding the problem that one seeks to solve is an essential initial step. In this paper, we propose computational methods for facilitating problem understanding through the task of recognizing the unknown in…
Suppose we need a deep collective analysis of an open scientific problem: there is a complex scientific hypothesis and a large online group of mutually unrelated experts with relevant private information of a diverse and unpredictable…
Let $p$ be an odd prime. In the paper we collect the author's various conjectures on congruences modulo $p$ or $p^2$, which are concerned with sums of binomial coefficients, Lucas sequences, power residues and special binary quadratic…
In this paper, we propose new generalizations of amicable numbers. We also give examples and prove properties of these new concepts.
We consider a somehow peculiar Token/Bucket problem which at first sight looks confusing and difficult to solve. The winning approach to solve the problem consists in going back to the simple and traditional methods to solve computer…
The generation of humor is an under-explored and challenging problem. Previous works mainly utilize templates or replace phrases to generate humor. However, few works focus on freer forms and the background knowledge of humor. The…
We present and prove a general form of Vandermonde's identity and use it as an alternative solution to a classic probability problem.
The old knowledge about interrelation among T-matrix, K-matrix and bare poles is summarized and put into modern perspective.
We spell two conundrums, one of physical and another of mathematical nature, and explain why one helps to elucidate the other