Related papers: Structuring Definitions in Mathematical Libraries
Matching logic is a logical framework for specifying and reasoning about programs using pattern matching semantics. A pattern is made up of a number of structural components and constraints. Structural components are syntactically matched,…
Autoformalization is the task of automatically translating mathematical content written in natural language to a formal language expression. The growing language interpretation capabilities of Large Language Models (LLMs), including in…
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…
Linear algebra is a major field of numerical computation and is widely applied. Most linear algebra libraries (in most programming languages) do not statically guarantee consistency of the dimensions of vectors and matrices, causing runtime…
Many interesting and useful symbolic computation algorithms manipulate mathematical expressions in mathematically meaningful ways. Although these algorithms are commonplace in computer algebra systems, they can be surprisingly difficult to…
We present a comprehensive programme analysing the decomposition of proof systems for non-classical logics into proof systems for other logics, especially classical logic, using an algebra of constraints. That is, one recovers a proof…
The continuous functional calculus is perhaps the most fundamental construction in the theory of operator algebras, especially $C^{*}$-algebras. Here we document our formalization of the continuous functional calculus in Lean, which…
Translating expressions between different logics and theorem provers is notoriously and often prohibitively difficult, due to the large differences between the logical foundations, the implementations of the systems, and the structure of…
Asking which sets are fixed-parameter tractable for a given parameterization constitutes much of the current research in parameterized complexity theory. This approach faces some of the core difficulties in complexity theory. By focussing…
Most modern formalisms used in Databases and Artificial Intelligence for describing an application domain are based on the notions of class (or concept) and relationship among classes. One interesting feature of such formalisms is the…
Logical frameworks provide natural and direct ways of specifying and reasoning within deductive systems. The logical framework LF and subsequent developments focus on finitary proof systems, making the formalization of circular proof…
Classification is an important goal in many branches of mathematics. The idea is to describe the members of some class of mathematical objects, up to isomorphism or other important equivalence in terms of relatively simple invariants. Where…
Large Language Models (LLMs) have demonstrated impressive capabilities in structured reasoning and symbolic tasks, with coding emerging as a particularly successful application. This progress has naturally motivated efforts to extend these…
Large language models (LLMs) can support scientific literature synthesis, but remain prone to hallucinated references, uneven coverage, and weakly grounded thematic organization. We evaluate whether bibliometric structure improves…
Categories and categorical structures are increasingly recognized as useful abstractions for modeling in science and engineering. To uniformly implement category-theoretic mathematical models in software, we introduce GATlab, a…
The interactive theorem prover Lean enables the verification of formal mathematical proofs and is backed by an expanding community. Central to this ecosystem is its mathematical library, mathlib4, which lays the groundwork for the…
The generality and pervasiness of category theory in modern mathematics makes it a frequent and useful target of formalization. It is however quite challenging to formalize, for a variety of reasons. Agda currently (i.e. in 2020) does not…
The emergence of tools based on artificial intelligence has also led to the need of producing explanations which are understandable by a human being. In most approaches, the system is considered a black box, making it difficult to generate…
Type theory plays an important role in foundations of mathematics as a framework for formalizing mathematics and a base for proof assistants providing semi-automatic proof checking and construction. Derivation of each theorem in type theory…
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…