Related papers: Proof in Context -- Web Editing with Rich, Modeles…
These notes provide a quick introduction to the Coq system and show how it can be used to define logical concepts and functions and reason about them. It is designed as a tutorial, so that readers can quickly start their own experiments,…
In order to work with mathematical content in computer systems, it is necessary to represent it in formal languages. Ideally, these are supported by tools that verify the correctness of the content, allow computing with it, and produce…
We implement a user-extensible ad hoc connection between the Lean proof assistant and the computer algebra system Mathematica. By reflecting the syntax of each system in the other and providing a flexible interface for extending…
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…
We investigate the proof theory of regular expressions with fixed points, construed as a notation for (omega-)context-free grammars. Starting with a hypersequential system for regular expressions due to Das and Pous, we define its extension…
The methodology of context-sensitive access to e-documents considers context as a problem model based on the knowledge extracted from the application domain, and presented in the form of application ontology. Efficient access to an…
Automated fact-checking based on machine learning is a promising approach to identify false information distributed on the web. In order to achieve satisfactory performance, machine learning methods require a large corpus with reliable…
We propose a novel approach for the formal verification of biological systems based on the use of a modal linear logic. We show how such a logic can be used, with worlds as instants of time, as an unified framework to encode both biological…
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…
In theorem proving, the task of selecting useful premises from a large library to unlock the proof of a given conjecture is crucially important. This presents a challenge for all theorem provers, especially the ones based on language…
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…
We present a framework for document-centric background generation with multi-page editing and thematic continuity. To ensure text regions remain readable, we employ a \emph{latent masking} formulation that softly attenuates updates in the…
While model checking has often been considered as a practical alternative to building formal proofs, we argue here that the theory of sequent calculus proofs can be used to provide an appealing foundation for model checking. Since the…
Recent years have seen the proliferation of disinformation and fake news online. Traditional approaches to mitigate these issues is to use manual or automatic fact-checking. Recently, another approach has emerged: checking whether the input…
This work discusses an approach to teach to mathematicians the importance and effectiveness of the application of Interactive Theorem Proving tools in their specific fields of interest. The approach aims to motivate the use of such tools…
Parsing is an important problem in computer science and yet surprisingly little attention has been devoted to its formal verification. In this paper, we present TRX: a parser interpreter formally developed in the proof assistant Coq,…
Document Visual Question Answering (DocVQA) remains challenging for existing Vision-Language Models (VLMs), especially under complex reasoning and multi-step workflows. Current approaches struggle to decompose intricate questions into…
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…
We present IntelliProof, an interactive system for analyzing argumentative essays through LLMs. IntelliProof structures an essay as an argumentation graph, where claims are represented as nodes, supporting evidence is attached as node…
Formal mathematics is mathematics done within the framework of a formal logic. It offers major benefits to mathematicians as well as to computing professionals, engineers, and scientists who use mathematics in their work. The standard…