Related papers: Voting Theory in the Lean Theorem Prover
Selection of input features such as relevant pieces of text has become a common technique of highlighting how complex neural predictors operate. The selection can be optimized post-hoc for trained models or incorporated directly into the…
This paper presents a comprehensive formalization of the von Neumann-Morgenstern (vNM) expected utility theorem using the Lean 4 interactive theorem prover. We implement the classical axioms of preference-completeness, transitivity,…
We propose a synthesis of the two proof styles of interactive theorem proving: the procedural style (where proofs are scripts of commands, like in Coq) and the declarative style (where proofs are texts in a controlled natural language, like…
We present a type theory with some proof-irrelevance built into the conversion rule. We argue that this feature is useful when type theory is used as the logical formalism underlying a theorem prover. We also show a close relation with the…
We show how voting may be viewed naturally from an algebraic perspective by viewing voting profiles as elements of certain well-studied $\mathbb{Q}S_n$-modules. By using only a handful of simple combinatorial objects (e.g., tabloids) and…
We consider the problem of how a trusted, but computationally bounded agent (a 'verifier') can learn to interact with one or more powerful but untrusted agents ('provers') in order to solve a given task. More specifically, we study the case…
Automatic verification deals with the validation by means of computers of correctness certificates. The related tools, usually called proof assistants or interactive provers, provide an interactive environment for the creation of formal…
In theorem provers based on dependent type theory such as Coq and Lean, induction is a fundamental proof method and induction tactics are omnipresent in proof scripts. Yet the ergonomics of existing induction tactics are not ideal: they do…
The mathematical study of voting, social choice theory, has traditionally only been applicable to choices among a few predetermined alternatives, but not to open-ended decisions such as collectively selecting a textual statement. We…
This paper develops an algorithmic-based approach for proving inductive properties of propositional sequent systems such as admissibility, invertibility, cut-elimination, and identity expansion. Although undecidable in general, these…
This paper describes a procedure that system developers can follow to translate typical mathematical representations of linearized control systems into logic theories. These theories are then used to verify system requirements and find…
Traditional approaches for validating molecular simulations rely on making software open source and transparent, incorporating unit testing, and generally employing human oversight. We propose an approach that eliminates software errors…
Formally verifying properties of software code has been a highly desirable task, especially with the emergence of LLM-generated code. In the same vein, they provide an interesting avenue for the exploration of formal verification and…
We define the concept of collaborative theorem proving and outline our plan to make it a reality. We believe that a successful implementation of collaborative theorem proving is a necessary prerequisite for the formal verification of large…
In this work, we present two results: The first result is the formalization of Tutte's theorem in Lean, a key theorem concerning matchings in graph theory. As this formalization is ready to be integrated in Lean's mathlib, it provides a…
We describe a formalization of forcing using Boolean-valued models in the Lean 3 theorem prover, including the fundamental theorem of forcing and a deep embedding of first-order logic with a Boolean-valued soundness theorem. As an…
Verifying mathematical proofs is difficult, but can be automated with the assistance of a computer. Autoformalization is the task of automatically translating natural language mathematics into a formal language that can be verified by a…
We present a method for using standard techniques from satisfiability checking to automatically verify and discover theorems in an area of economic theory known as ranking sets of objects. The key question in this area, which has important…
We present an extension to the $\mathtt{mathlib}$ library of the Lean theorem prover formalizing the foundations of computability theory. We use primitive recursive functions and partial recursive functions as the main objects of study, and…
Theorem proving is a fundamental aspect of mathematics, spanning from informal reasoning in natural language to rigorous derivations in formal systems. In recent years, the advancement of deep learning, especially the emergence of large…