Related papers: Online Generation of Proofs Without Words
MathGloss is a project to create a knowledge graph (KG) for undergraduate mathematics from text, automatically, using modern natural language processing (NLP) tools and resources already available on the web. MathGloss is a linked database…
We outline a program in the area of formalization of mathematics to automate theorem proving in algebra and algebraic geometry. We propose a construction of a dictionary between automated theorem provers and (La)TeX exploiting syntactic…
The unique capabilities of Large Language Models (LLMs), such as the natural language text generation ability, position them as strong candidates for providing explanation for recommendations. However, despite the size of the LLM, most…
Teaching precise mathematical reasoning can be very hard. It is very easy for a student to make a subtle mistake in a proof which invalidates it, but it is often hard for the teacher to pinpoint and explain the problem in the (often…
In settings from fact-checking to question answering, we frequently want to know whether a collection of evidence (premises) entails a hypothesis. Existing methods primarily focus on the end-to-end discriminative version of this task, but…
We present Cobra, a modern proof presentation framework, leveraging cutting-edge presentation technology together with a state of the art interactive theorem prover to present formalized mathematics as active documents. Cobra provides both…
Due to their numerous advantages, formal proofs and proof assistants, such as Coq, are becoming increasingly popular. However, one disadvantage of using proof assistants is that the resulting proofs can sometimes be hard to read and…
With help of a compact Prolog-based theorem prover for Intuitionistic Propositional Logic, we synthesize minimal assumptions under which a given formula formula becomes a theorem. After applying our synthesis algorithm to cover basic…
While proof is a central component of postsecondary mathematical study, proof construction has historically posed significant difficulties for students who intend to earn mathematics degrees at the undergraduate level. This work is…
Understanding, finding, or even deciding on the existence of real solutions to a system of equations is a very difficult problem with many applications. While it is hopeless to expect much in general, we know a surprising amount about these…
We introduce a term algebra as a new formal specification language for the coordinating architectures of distributed systems consisting of a finite yet unbounded number of components. The language allows to describe infinite sets of systems…
We develop a linear-algebraic framework for dimensional analysis in systems with constraints, particularly when variables are numerous or related by implicit relations so that direct elimination is impractical. By expressing both…
Mechanized theorem proving is becoming the basis of reliable systems programming and rigorous mathematics. Despite decades of progress in proof automation, writing mechanized proofs still requires engineers' expertise and remains labor…
A number of flexible tactic-based logical frameworks are nowadays available that can implement a wide range of mathematical theories using a common higher-order metalanguage. Used as proof assistants, one of the advantages of such powerful…
Automatic question generation is one of the most challenging tasks of Natural Language Processing. It requires "bidirectional" language processing: firstly, the system has to understand the input text (Natural Language Understanding) and it…
Automatically generating debates is a challenging task that requires an understanding of arguments and how to negate or support them. In this work we define debate trees and paths for generating debates while enforcing a high level…
Automated Theorem Proving (ATP) is an established branch of Artificial Intelligence. The purpose of ATP is to design a system which can automatically figure out an algorithm either to prove or disprove a mathematical claim, on the basis of…
Mathematical proofs are both paradigms of certainty and some of the most explicitly-justified arguments that we have in the cultural record. Their very explicitness, however, leads to a paradox, because the probability of error grows…
Several approaches exist to data-mining big corpora of formal proofs. Some of these approaches are based on statistical machine learning, and some -- on theory exploration. However, most are developed for either untyped or simply-typed…
LangPro is an automated theorem prover for natural language (https://github.com/kovvalsky/LangPro). Given a set of premises and a hypothesis, it is able to prove semantic relations between them. The prover is based on a version of analytic…