Related papers: It's Common Knowledge
Machine learning (ML) in its current form implies that an answer to any problem can be well approximated by a function of a very peculiar form: a specially adjusted iteration of Heavyside theta-functions. It is natural to ask if the answers…
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…
Commonsense knowledge about everyday concepts is an important asset for AI applications, such as question answering and chatbots. Recently, we have seen an increasing interest in the construction of structured commonsense knowledge bases…
This paper examines the classical matching distribution arising in the "problem of coincidences". We generalise the classical matching distribution with a preliminary round of allocation where items are correctly matched with some fixed…
Two Turing Machines may be able to answer questions about each other that they cannot answer about themselves.
A novel approach to an old symmetry problem is developed. A new proof is given for the following symmetry problem, studied earlier.
We survey recent developments in the theory of achievement sets and present a substantial collection of open problems.
"The hardest logic puzzle ever" presented by George Boolos became a target for philosophers and logicians who tried to modify it and make it even tougher. I propose further modification of the original puzzle where part of the available…
We provide a list of (mainly unsolved) problems in ordered and orderable groups. These were originally compiled 10 years ago by the last two authors. New problems have been added to the list. Progress on some of these is noted and…
In this short article, we present a solution to one of the probability puzzles that Daniel Litt, a mathematician at the University of Toronto, posted on his X account earlier this year. The main goal of this note is to show how some of the…
Recently several datasets have been proposed to encourage research in Question Answering domains where commonsense knowledge is expected to play an important role. Recent language models such as ROBERTA, BERT and GPT that have been…
This report concerns the information content of a graph, optionally conditional on one or more background, "common knowledge" graphs. It describes an algorithm to estimate this information content, and includes some examples based on…
The general solution to the Complex Bateman equation is constructed. It is given in implicit form in terms of a functional relationship for the unknown function. The known solution of the usual Bateman equation is recovered as a special…
Considering collaborative patent development, we provide micro-level evidence for innovation through exchanges of differentiated knowledge. Knowledge embodied in a patent is proxied by word pairs appearing in its abstract, while novelty is…
This is a collection of open problems in geometry that I think of as puzzles: they stick to my brain -- I see many grips, but no spare hands. Puzzle-charm is the only criterion for including a problem here; importance is ignored.
I discuss some general aspects of the creation, interpretation, and reception of mathematics as a part of civilization and culture.
An technically interesting proof of a known theorem.
New understandings of the functioning of human brains engaged in mathematics raise interesting questions for mathematics educators. Novel lines of research are suggested by neuroscientific findings, and new light is shed on some…
By investigating a recurrence relation about functions, we first give alternative proofs of various identities on Fibonacci numbers and Lucas numbers, and then, make certain well known identities visible via certain trivalent graph…
This paper presents experiments on common knowledge logic, conducted with the help of the proof assistant Coq. The main feature of common knowledge logic is the eponymous modality that says that a group of agents shares a knowledge about a…