Related papers: Point-and-write --- Documenting Formal Mathematics…
This thesis is devoted to the study of a calculus that describes the application of conditional rewriting rules and the obtained results at the same level of representation. We introduce the rewriting calculus, also called the rho-calculus,…
We present components of an AI-assisted academic writing system including citation recommendation and introduction writing. The system recommends citations by considering the user's current document context to provide relevant suggestions.…
Mathematical documents written in LaTeX often contain ambiguities. We can resolve some of them via semantic markup using, e.g., sTeX, which also has other potential benefits, such as interoperability with computer algebra systems, proof…
We recently presented the so-called allagmatic method, which includes a system metamodel providing a framework for describing, modelling, simulating, and interpreting complex systems. Its development and programming was guided by…
We study the formalization of a collection of documents created for a Software Engineering project from an MKM perspective. We analyze how document and collection markup formats can cope with an open-ended, multi-dimensional space of…
When formalizing proofs with interactive theorem provers, it often happens that extra background knowledge (declarative or procedural) about mathematical concepts is employed without the formalizer explicitly invoking it, to help the…
Foundations of formal languages, as subfield of theoretical computer science, are part of typical upper secondary education curricula. There is very little research on the potential difficulties that students at this level have with this…
We explore the features of a user interface where formal proofs can be built through gestural actions. In particular, we show how proof construction steps can be associated to drag-and-drop actions. We argue that this can provide quick and…
In applied mathematics and related disciplines, the modeling-simulation-optimization workflow is a prominent scheme, with mathematical models and numerical algorithms playing a crucial role. For these types of mathematical research data,…
The purpose of this manuscript is to gather together a large amount of source material pertaining to women in mathematics, from studies of girls in elementary school through data on females winning prizes for mathematical research. Along…
In this paper are briefly outlined the motivations, mathematical ideas in use, pre-formalization and assumptions, object-as-functor construction, `soft' types and concept constructions, case study for concepts based on variable domains,…
We discuss a formal system of mathematics. We use it to construct the natural numbers.
Informal mathematics has been central to modern large language model (LLM) reasoning, offering flexibility and enabling efficient construction of arguments. However, purely informal reasoning is prone to logical gaps and subtle errors that…
A standard informal method for analyzing the asymptotic complexity of a program is to extract a recurrence that describes its cost in terms of the size of its input, and then to compute a closed-form upper bound on that recurrence. We give…
Formal Methods tools will never have as many users as tools for popular programming languages and so the effort spent on constructing Integrated Development Environments (IDEs) will be orders of magnitudes lower than that of programming…
Most existing computational tools for assumption-based argumentation (ABA) focus on so-called flat frameworks, disregarding the more general case. In this paper, we study an instantiation-based approach for reasoning in possibly non-flat…
This paper shows an overview of a research project for integrating formal methods in popular practices for software development in Mexico. The article shows only the main results from the survey about methods and practices and an overview…
Web Services provide interoperable mechanisms for describing, locating and invoking services over the Internet; composition further enables to build complex services out of simpler ones for complex B2B applications. While current studies on…
We introduce a framework for lightweight dependency syntax annotation. Our formalism builds upon the typical representation for unlabeled dependencies, permitting a simple notation and annotation workflow. Moreover, the formalism encourages…
The Mathematization project investigates students' use of mathematical tools across the undergraduate physics curriculum. As a part of this project, we look at intermediate mechanics students' written homework solutions to understand how…