Related papers: Formal Mathematics on Display: A Wiki for Flyspeck
Object placement assessment (OPA) aims to predict the rationality score of a composite image in terms of the placement (e.g., scale, location) of inserted foreground object. However, given a pair of scaled foreground and background, to…
As automated reasoning systems advance rapidly, there is a growing need for research-level formal mathematical problems to accurately evaluate their capabilities. To address this, we present Formal Conjectures, an evolving benchmark of…
In AI-rich higher education, polished written mathematics has become easier to produce than trustworthy evidence of understanding. This article develops a human-scale methodology for service mathematics, with informatics as its main running…
Reliable verification of proofs remains a bottleneck for training and evaluating AI systems on hard mathematical reasoning. Fully formal proofs, in languages like Lean, are easy to verify because they are unambiguous and modular. Most…
Ontology Learning (OL) is the computational task of generating a knowledge base in the form of an ontology given an unstructured corpus whose content is in natural language (NL). Several works can be found in this area most of which are…
We present an implementation of algorithms for the symbolic integration of hyperlogarithms multiplied by rational functions in the computer algebra system FORM. This implementation encompasses cases where hyperlogarithms have rational…
This book explores an alternative to the current dominant paradigm where a discrete computer model is constructed as an attempt to approximate some continuum theory. We focus on a class of discrete computer models that are based on simple…
The evaluation of academic theses is a cornerstone of higher education, ensuring rigor and integrity. Traditional methods, though effective, are time-consuming and subject to evaluator variability. This paper presents RubiSCoT, an…
Formal concept analysis (FCA) is a well-founded method for data analysis and has many applications in data mining. Pattern structures is an extension of FCA for dealing with complex data such as sequences or graphs. However the…
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…
Autoformalization has emerged as a term referring to the automation of formalization - specifically, the formalization of mathematics using interactive theorem provers (proof assistants). Its rapid development has been driven by progress in…
The paper presents the second part of a precise description of the prototype that has been developed in the course of the ISAC project over the last two decades. This part describes the "specify-phase", while the first part describing the…
Many concepts of physical optics can be visually illustrated on a relatively simple optical setup in a table-top format, not requiring any very specific equipment. Diffraction, interferences, speckle, image formation, Fourier optics,…
Formal Concept Analysis (FCA) is a mathematical framework for knowledge representation and discovery. It performs a hierarchical clustering over a set of objects described by attributes, resulting in conceptual structures in which objects…
Active Logic Documents (ALD) are web pages which incorporate embedded Prolog engines that run locally within the browser. ALD offers both a very easy way to add click-to-run capabilities to any kind of teaching materials, independently of…
Proust is a small Racket program offering rudimentary interactive assistance in the development of verified proofs for propositional and predicate logic. It is constructed in stages, some of which are done by students before using it to…
The Gisela framework for declarative programming was developed with the specific aim of providing a tool that would be useful for knowledge representation and reasoning within real-world applications. To achieve this, a complete integration…
Intelligent tutoring systems have long enabled automated immediate feedback on student work when it is presented in a tightly structured format and when problems are very constrained, but reliably assessing free-form mathematical reasoning…
One of the scientific objectives of the Ooty Wide Field Array(OWFA) is to observe the redshifted HI emission from z ~ 3.35. Although predictions spell out optimistic outcomes in reasonable integration times, these studies were based purely…
A theory graph is a network of axiomatic theories connected with meaning-preserving mappings called theory morphisms. Theory graphs are well suited for organizing large bodies of mathematical knowledge. Traditional and formal proofs do not…