Related papers: Testing the equivalence principle: why and how?
We present a unifying framework for type systems for process calculi. The core of the system provides an accurate correspondence between essentially functional processes and linear logic proofs; fragments of this system correspond to…
We provide a counterexample to a lemma used in a recent tentative improvement of the the Pin-Frankl bound for synchronizing automata. This example naturally leads us to formulate an open question, whose answer could fix the line of proof,…
Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles…
Theoretical physics is the search for simple and universal mathematical descriptions of the natural world. In contrast, much of modern biology is an exploration of the complexity and diversity of life. For many, this contrast is prima facie…
This essay considers the special character of mathematical reasoning, and draws on observations from interactive theorem proving and the history of mathematics to clarify the nature of formal and informal mathematical language. It proposes…
This note tries to show that a re-examination of a first course in analysis, using the more sophisticated tools and approaches obtained in later stages, can be a real fun for experts, advanced students, etc. We start by going to the…
A problem faced by many instructors is that of designing exams that accurately assess the abilities of the students. Typically these exams are prepared several days in advance, and generic question scores are used based on rough…
One main goal of argumentation theory is to evaluate arguments and to determine whether they should be accepted or rejected. When there is no clear answer, a third option, being undecided, has to be taken into account. Indecision is often…
A significant amount of research has considered mathematical proofs, the students who learn them, and the instructors that teach them, from a variety of perspectives. This paper considers this topic from four main perspectives: students'…
Recent advances in preference optimization have demonstrated significant potential for improving mathematical reasoning capabilities in large language models (LLMs). While current approaches leverage high-quality pairwise preference data…
Property testing is concerned with the design of algorithms making a sublinear number of queries to distinguish whether the input satisfies a given property or is far from having this property. A seminal paper of Alon, Krivelevich, Newman,…
I review the reason for considering the prime purpose of the program of measurements of the fundamental parameters of cosmology to be the tests of cosmological models. I comment on the philosophy by which we are approaching this goal, offer…
The selection process of proposals is a crucial component of scientific progress and innovations. Limited resources must be allocated in the most effective way to maximise advancements and the production of new knowledge, especially as it…
We develop models to classify desirable evidence and desirable reasoning revisions in student argumentative writing. We explore two ways to improve classifier performance - using the essay context of the revision, and using the feedback…
Which mechanisms are simple to play? When is it easy for participants to see that a mechanism is incentive-compatible? I will start by explaining how and why economists came to ask these questions. Then I will discuss three recent answers,…
This expository note describes two convenient techniques in the context of homotopy type theory for proving and formalizing that a given map is an equivalence. The first technique decomposes the map as a series of basic equivalences, while…
This paper investigates the strict comparison theorem under the framework of $G$-expectation, i.e., let $X\leq Y$ q.s., if $X,Y$ satisfy some additional conditions, then $\E[X]<\E[Y]$.
In this work we generalize standard Decision Theory by assuming that two outcomes can also be incomparable. Two motivating scenarios show how incomparability may be helpful to represent those situations where, due to lack of information,…
We propose an algorithm that test membership for regular expressions and show that the algorithm is correct. This algorithm is written in the style of a sequent proof system. The advantage of this algorithm over traditional ones is that the…
Argumentation theory is a powerful paradigm that formalizes a type of commonsense reasoning that aims to simulate the human ability to resolve a specific problem in an intelligent manner. A classical argumentation process takes into account…