Related papers: Proof Mining with Dependent Types
Interactive theorem provers such as Coq are powerful tools to formally guarantee the correctness of software. However, using these tools requires significant manual effort and expertise. While Large Language Models (LLMs) have shown promise…
The assumptions needed to prove Cox's Theorem are discussed and examined. Various sets of assumptions under which a Cox-style theorem can be proved are provided, although all are rather strong and, arguably, not natural.
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…
Automated theorem provers and formal proof assistants are general reasoning systems that are in theory capable of proving arbitrarily hard theorems, thus solving arbitrary problems reducible to mathematics and logical reasoning. In…
Expert systems applications that involve uncertain inference can be represented by a multidimensional contingency table. These tables offer a general approach to inferring with uncertain evidence, because they can embody any form of…
Dependently typed programming languages have become increasingly relevant in recent years. They have been adopted in industrial strength programming languages and have been extremely successful as the basis for theorem provers. There are…
Differentiable logics are a family of quantitative logics originated in the machine learning literature. Because of their origin, differentiable logics often come equipped with analytic properties that guarantee that they are…
Building machines that can understand text like humans is an AI-complete problem. A great deal of research has already gone into this, with astounding results, allowing everyday people to discuss with their telephones, or have their reading…
A type theory is presented that combines (intuitionistic) linear types with type dependency, thus properly generalising both intuitionistic dependent type theory and full linear logic. A syntax and complete categorical semantics are…
This paper introduces a new methodology for the complexity analysis of higher-order functional programs, which is based on three ingredients: a powerful type system for size analysis and a sound type inference procedure for it, a ticking…
Understanding and creating mathematics using natural mathematical language - the mixture of symbolic and natural language used by humans - is a challenging and important problem for driving progress in machine learning. As a step in this…
In this paper, we present a formalization of Kozen's propositional modal $\mu$-calculus, in the Calculus of Inductive Constructions. We address several problematic issues, such as the use of higher-order abstract syntax in inductive sets in…
Dependently typed languages such as Coq are used to specify and verify the full functional correctness of source programs. Type-preserving compilation can be used to preserve these specifications and proofs of correctness through…
Proof assistants and programming languages based on type theories usually come in two flavours: one is based on the standard natural deduction presentation of type theory and involves eliminators, while the other provides a syntax in…
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…
Artificial intelligence assisted mathematical proof has become a highly focused area nowadays. One key problem in this field is to generate formal mathematical proofs from natural language proofs. Due to historical reasons, the formal proof…
The successful analysis of argumentative techniques from user-generated text is central to many downstream tasks such as political and market analysis. Recent argument mining tools use state-of-the-art deep learning methods to extract and…
Text mining is about looking for patterns in natural language text, and may be defined as the process of analyzing text to extract information from it for particular purposes. In previous work, we claimed that compression is a key…
There are various kinds of type analysis of logic programs. These include for example inference of types that describe an over-approximation of the success set of a program, inference of well-typings, and abstractions based on given types.…
This work proposes a dependent type theory that combines functions and session-typed processes (with value dependencies) through a contextual monad, internalising typed processes in a dependently-typed lambda-calculus. The proposed…