This work gives the first foundational treatment of proof repair, focusing in particular on type-theoretic proof repair in response to changes in datatypes, and formalizes and proves that the core component of this proof repair algorithm—a “configuration”—is exactly an algebra isomorphism.
Pistis is introduced, an agentic, oracle-guided proof search that produces formal Lean proofs that satisfy faithfulness conditions and can accept or refute natural language proofs written by humans or AI, demonstrating that faithful formalization is useful as a proof-checking tool.
Tadd Mao, Tianjun Zhong, Dhruva Arekar et al.· 1 citation
The Ideal Proof System, introduced by Grochow and Pitassi, is the focus of this talk, which will explore the IPS proof system, its connections to algebraic complexity, and recent developments in the area.
N. Limaye· International Colloquium on...· 0 citations
This paper investigates the question: what is a formal logical proof (in general—as opposed to: what is a formal proof in this or that specific proof system)? I begin by setting out a core conception of formal proof and substantiating its designation as ‘core’. The heart of this conception is that there must be an ef...
Nicholas J. J. Smith· The Review of Symbolic Logic· 0 citations
This paper provides a setting in which congruences can be treated as actual equalities, mirroring the informal practice of mathematicians and eliminating the need to use the lemmas typically required for formal congruence proofs.
Dale A. Miller· International Conference on...· 0 citations
It is shown that the epsilon calculus provides a natural framework for analyzing tolerance of falsity in proofs and for identifying conditions under which an incorrect proof can be semantically repaired.
This work provides a categorical treatment of Canetti's Universal Composability (UC) framework for systems with a static number of parties and sessions, often termed UC for static systems, yielding four benefits, including graphically verified formulation of the composition theorem.
P. Farshim, M. Karvonen, Andre Knispel et al.· IACR Cryptology ePrint Archi...· 0 citations
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