Related papers: Proof-checking Euclid
Uniform proofs are sequent calculus proofs with the following characteristic: the last step in the derivation of a complex formula at any stage in the proof is always the introduction of the top-level logical symbol of that formula. We…
This paper introduces ProofCloud, a proof retrieval engine for verified proofs in higher order logic. It provides a fast proof searching service for mathematicians and computer scientists for the reuse of proofs and proof packages. In…
Higher-order correlation functions of the large-scale galaxy distribution offer access to information beyond that contained in standard 2-point statistics such as the power spectrum. In this work we assess this potential for the…
With today's quantum processors venturing into regimes beyond the capabilities of classical devices [1-3], we face the challenge to verify that these devices perform as intended, even when we cannot check their results on classical…
Real-life conjectures do not come with instructions saying whether they they should be proven or, instead, refuted. Yet, as we now know, in either case the final argument produced had better be not just convincing but actually verifiable in…
A cyclic proof system allows us to perform inductive reasoning without explicit inductions. We propose a cyclic proof system for HFLN, which is a higher-order predicate logic with natural numbers and alternating fixed-points. Ours is the…
This is a survey on propositional proof complexity aimed at introducing the basics of the field with a particular focus on a method known as feasible interpolation. This method is used to construct "hard theorems" for several proof systems…
Mathematical proofs are a cornerstone of control theory, and it is important to get them right. Deduction systems can help with this by mechanically checking the proofs. However, the structure and level of detail at which a proof is…
We present LISA, a proof system and proof assistant for constructing proofs in schematic first-order logic and axiomatic set theory. The logical kernel of the system is a proof checker for first-order logic with equality and schematic…
Formal verification provides mathematical guarantees that a software is correct. Design-level verification tools ensure software specifications are correct, but they do not expose defects in actual implementations. For this purpose,…
Constructive-deductive method for plane Euclidean geometry is proposed and formalized within Coq Proof Assistant. This method includes both postulates that describe elementary constructions by idealized geometric tools (pencil, straightedge…
The idea of assisting teachers with technological tools is not new. Mathematics in general, and geometry in particular, provide interesting challenges when developing educative softwares, both in the education and computer science aspects.…
Checking the soundness of cyclic induction reasoning for first-order logic with inductive definitions (FOLID) is decidable but the standard checking method is based on an exponential complement operation for B\"uchi automata. Recently, we…
We provide a simple and efficient algorithm for computing the Euclidean projection of a point onto the capped simplex---a simplex with an additional uniform bound on each coordinate---together with an elementary proof. Both the MATLAB and…
We advocates here the use of (mathematical) logic for systems biology, as a unified framework well suited for both modeling the dynamic behaviour of biological systems, expressing properties of them, and verifying these properties. The…
In this chapter, we propose some future directions of work, potentially beneficial to Mathematics and its foundations, based on the recent import of methodology from the theory of programming languages into proof theory. This scientific…
A proof of quantumness is an efficiently verifiable interactive test that an efficient quantum computer can pass, but all efficient classical computers cannot (under some cryptographic assumption). Such protocols play a crucial role in the…
The two major systems of formal verification are model checking and algebraic model-based testing. Model checking is based on some form of temporal logic such as linear temporal logic (LTL) or computation tree logic (CTL). One powerful and…
We give three new proofs of the triangle inequality in Euclidean Geometry. There seems to be only one known proof at the moment. It is due to properties of triangles, but our proofs are due to circles or ellipses. We aim to prove the…
Inductive theorem proving is an important long-standing challenge in computer science. In this extended abstract, we first summarize the recent developments of proof by induction for Isabelle/HOL. Then, we propose united reasoning, a novel…