Related papers: Formal Mathematics on Display: A Wiki for Flyspeck
AI for Mathematics (AI4Math) is not only intriguing intellectually but also crucial for AI-driven discovery in science, engineering, and beyond. Extensive efforts on AI4Math have mirrored techniques in NLP, in particular, training large…
An introductory formal languages course exposes advanced undergraduate and early graduate students to automata theory, grammars, constructive proofs, computability, and decidability. Programming students find these topics to be challenging…
Education in the practical applications of logic and proving such as the formal specification and verification of computer programs is substantially hampered by the fact that most time and effort that is invested in proving is actually…
In recent years, the interest in using proof assistants to formalise and reason about mathematics and programming languages has grown. Type-logical grammars, being closely related to type theories and systems used in functional programming,…
FORM, a symbolic manipulation system, has been widely used in a lot of calculations for High Energy Physics due to its high performance and fficient design. Mathematica, another computational software program, has also widely been used, but…
Machine reading comprehension (MRC) that requires discrete reasoning involving symbolic operations, e.g., addition, sorting, and counting, is a challenging task. According to this nature, semantic parsing-based methods predict interpretable…
Elfe is an interactive system for teaching basic proof methods in discrete mathematics. The user inputs a mathematical text written in fair English which is converted to a special data-structure of first-order formulas. Certain proof…
We argue that the implementation and verification of compilers for functional programming languages are greatly simplified by employing a higher-order representation of syntax known as Higher-Order Abstract Syntax or HOAS. The underlying…
Formal reasoning and automated theorem proving constitute a challenging subfield of machine learning, in which machines are tasked with proving mathematical theorems using formal languages like Lean. A formal verification system can check…
We propose a simple, yet expressive proof representation from which proofs for different proof assistants can easily be generated. The representation uses only a few inference rules and is based on a frag- ment of first-order logic called…
Communication is a prerequisite for collaboration. When scaling networks of AI-powered agents, communication must be versatile, efficient, and portable. These requisites, which we refer to as the Agent Communication Trilemma, are hard to…
We present several steps towards large formal mathematical wikis. The Coq proof assistant together with the CoRN repository are added to the pool of systems handled by the general wiki system described in \cite{DBLP:conf/aisc/UrbanARG10}. A…
We introduce a large-scale dataset of math word problems and an interpretable neural math problem solver that learns to map problems to operation programs. Due to annotation challenges, current datasets in this domain have been either…
Explicit Semantic Analysis (ESA) is a technique used to represent a piece of text as a vector in the space of concepts, such as Articles found in Wikipedia. We propose a methodology to incorporate knowledge of Inter-relatedness between…
With the growth of fake news and disinformation, the NLP community has been working to assist humans in fact-checking. However, most academic research has focused on model accuracy without paying attention to resource efficiency, which is…
The paper presents a software tool for analysis and interactive engagement in various logical reasoning tasks. A first feature of the program consists in providing an interface for working with logic-specific repositories of formal…
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…
I describe preliminary experiments in documenting Excelsior versions of spreadsheets using semantic wikis and literate programming. The objective is to create well-structured and comprehensive documentation, easy to use by those unfamiliar…
The ever-growing complexity of mathematical proofs makes their manual verification by mathematicians very cognitively demanding. Autoformalization seeks to address this by translating proofs written in natural language into a formal…
Teaching college students how to write rigorous proofs is a critical objective in courses that introduce formal reasoning. Over the course of several years, we have developed a mechanically-checkable style of calculational reasoning that we…