Related papers: Hat Puzzles
We provide here a dataset for tasks related to natural language understanding and natural language inference. The dataset contains logical puzzles in natural language from three domains: comparing puzzles, knighs and knaves, and zebra…
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.
Large Language Models (LLMs) are revolutionizing the field of computing education with their powerful code-generating capabilities. Traditional pedagogical practices have focused on code writing tasks, but there is now a shift in importance…
For many years, I have been collecting math jokes and posting them on my website. I have more than 400 jokes there. In this paper, which is an extended version of my talk at the G4G15, I would like to present 66 of them.
This article gives some memories of Thomas Hales of his years at Princeton as a graduate student under Robert Langlands. It has been prepared for the book "The Genesis of Langlands' Program," edited by Dr. Julia Mueller and Dr. Freydoon…
We evaluate LLMs' language understanding capacities on simple inference tasks that most humans find trivial. Specifically, we target (i) grammatically-specified entailments, (ii) premises with evidential adverbs of uncertainty, and (iii)…
This short note is devoted to the unraveling of the hidden interactivity of ordinary games which is an artefact of predictions of the behaviour of other players by the fixed player and describes deviations of their real behaviour from such…
In this paper, we present a new, graph-based modeling approach and a polynomial-sized linear programming (LP) formulation of the Boolean satisfiability problem (SAT). The approach is illustrated with a numerical example.
Most conference papers present new results, but this paper will focus more on opportunities for the audience to make their own contributions. This paper is intended to challenge the community to think more broadly about what we can do with…
In connection to the development of the field of Combinatorics on Words, we present a list of open problems and conjectures that were stated during the ten last meetings WORDS. We wish to continually update the present document by adding…
Program transformation is an appealing technique which allows to improve run-time efficiency, space-consumption, and more generally to optimize a given program. Essentially, it consists of a sequence of syntactic program manipulations which…
We define a novel textual entailment task that requires inference over multiple premise sentences. We present a new dataset for this task that minimizes trivial lexical inferences, emphasizes knowledge of everyday events, and presents a…
The Winograd Schema Challenge is both a commonsense reasoning and natural language understanding challenge, introduced as an alternative to the Turing test. A Winograd schema is a pair of sentences differing in one or two words with a…
As Large Language Models (LLMs) become increasingly embedded in empirical research workflows, their use as analytical tools for quantitative or qualitative data raises pressing concerns for scientific integrity. This opinion paper draws a…
Several variations of hat guessing games have been popularly discussed in recreational mathematics. In a typical hat guessing game, after initially coordinating a strategy, each of $n$ players is assigned a hat from a given color set.…
The outline of a programme for restructuring mathematical logic. We explain what we mean by "restructuring" and carry out exemplary parts of the programme.
We present a variation of the water puzzle, which is related to a simple model of marginal utility. The problem has an intriguing solution and can be extended in several directions.
When we want to compute the probability of a query from a Probabilistic Answer Set Program, some parts of a program may not influence the probability of a query, but they impact on the size of the grounding. Identifying and removing them is…
This paper discusses several linear algebra activities designed to help enhance students' skills in collaborating, exploring mathematics, and linking together abstract and visual ways of approaching mathematics. Most of these activities are…
The primary aim of this paper is to suggest questions for future discourse and research of specialized programming courses in the Humanities. Specifically I ask whether specialized courses promote the production of fragile programming…