Related papers: Voting Theory in the Lean Theorem Prover
We study the effect of strategic behavior in iterative voting for multiple issues under uncertainty. We introduce a model synthesizing simultaneous multi-issue voting with Meir, Lev, and Rosenschein (2014)'s local dominance theory and…
Mathematics formalisation is the task of writing mathematics (i.e., definitions, theorem statements, proofs) in natural language, as found in books and papers, into a formal language that can then be checked for correctness by a program. It…
We formalize Hall's Marriage Theorem in the Lean theorem prover for inclusion in mathlib, which is a community-driven effort to build a unified mathematics library for Lean. One goal of the mathlib project is to contain all of the topics of…
In this paper we present a new "external checker" for the Lean theorem prover, written in Lean itself. This is the first complete typechecker for Lean 4 other than the reference implementation in C++ used by Lean itself, and our new checker…
We describe a generalization of the voter model on complex networks that encompasses different sources of degree-related heterogeneity and that is amenable to direct analytical solution by applying the standard methods of heterogeneous…
Using multisets, we develop novel techniques for mechanizing the proofs of the synthesis conjectures for list-sorting algorithms, and we demonstrate them in the Theorema system. We use the classical principle of extracting the algorithm as…
The free-variable tableau method has been widely used in order to automate proofs in multiple kinds of logics. Many automated theorem provers rely on this approach, either because it is the only available method-e.g., in certain modal…
Noting that lemmas are a key feature of mathematics, we engage in an investigation of the role of lemmas in automated theorem proving. The paper describes experiments with a combined system involving learning technology that generates…
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…
Static verification relying on an automated theorem prover can be very slow and brittle: since static verification is undecidable, correct code may not pass a particular static verifier. In this work we use metaprogramming to generate code…
Solving mathematical problems using computer-verifiable languages like Lean has significantly impacted the mathematical and computer science communities. State-of-the-art methods utilize a single Large Language Model (LLM) to generate…
A recent work by Hern\'andez et al. introduced a networked voting rule supported by a trust-based social network, where indications of possible representatives were based on individuals opinions. Individual contributions went beyond a…
Latane social impact theory predicts recruitment and supportive interactions being responsible for opinion formation. So far only recruitment interactions were considered in the voter models. Here we consider a noisy voter model with…
To take advantage of Large Language Model in theorem formalization and proof, we propose a reinforcement learning framework to iteratively optimize the pretrained LLM by rolling out next tactics and comparing them with the expected ones.…
Different theorem provers tend to produce proof objects in different formats and this is especially the case for modal logics, where several deductive formalisms (and provers based on them) have been presented. This work falls within the…
Emergent collective group processes and capabilities have been studied through analysis of transactive memory, measures of group task performance, and group intelligence, among others. In their approach to collective behaviors, these…
A number of flexible tactic-based logical frameworks are nowadays available that can implement a wide range of mathematical theories using a common higher-order metalanguage. Used as proof assistants, one of the advantages of such powerful…
Formal, automated theorem proving has long been viewed as a challenge to artificial intelligence. We introduce here a new approach to computer theorem proving, one that employs specialized language models for Lean4 proof generation combined…
Multiwinner voting rules are used to select a small representative subset of candidates or items from a larger set given the preferences of voters. However, if candidates have sensitive attributes such as gender or ethnicity (when selecting…
This article unpacks the design choices behind longstanding and newly proposed computational frameworks aimed at finding common grounds across collective preferences and examines their potential future impacts, both technically and…