Results 21 to 30 of about 1,881,310 (251)
A formal proof of the independence of the continuum hypothesis [PDF]
Certified Programs and Proofs, 2020 We describe a formal proof of the independence of the continuum hypothesis (CH) in the Lean theorem prover. We use Boolean-valued models to give forcing arguments for both directions, using Cohen forcing for the consistency of ¬ CH and a σ-closed forcing
Jesse Michael Han, Floris van Doorn
semanticscholar +1 more source
Is Mathematical Logic Really Necessary in Teaching Mathematical Proofs? [PDF]
Athens Journal of Education, 2020 As it is already observed by mathematicians and educators, there is a discrepancy between the formal techniques of mathematical logic and the informal techniques of mathematics in regards to proof.
Michael Aristidou
doaj +1 more source
A formal proof and simple explanation of the QuickXplain algorithm
Artificial Intelligence Review, 2022 In his seminal paper of 2004, Ulrich Junker proposed the QuickXplain algorithm, which provides a divide-and-conquer computation strategy to find within a given set an irreducible subset with a particular (monotone) property.
P. Rodler
semanticscholar +1 more source
Integration of Formal Proof into Unified Assurance Cases with Isabelle/SACM [PDF]
Formal Aspects of Computing, 2020 Assurance cases are often required to certify critical systems. The use of formal methods in assurance can improve automation, increase confidence, and overcome errant reasoning.
S. Foster +4 more
semanticscholar +1 more source
Principia: An International Journal of Epistemology, 2022 When adopting a sound logical system, reasonings made within this system are correct. The situation with reasonings expressed, at least in part, with natural language is much more ambiguous. One way to be certain of the correctness of these reasonings is
Mario Bacelar Valente
doaj +1 more source
A formal proof of PAC learnability for decision stumps
Certified Programs and Proofs, 2021 We present a formal proof in Lean of probably approximately correct (PAC) learnability of the concept class of decision stumps. This classic result in machine learning theory derives a bound on error probabilities for a simple type of classifier.
Joseph Tassarotti +3 more
semanticscholar +1 more source
Logic for exact real arithmetic [PDF]
Logical Methods in Computer Science, 2021 Continuing earlier work of the first author with U. Berger, K. Miyamoto and H. Tsuiki, it is shown how a division algorithm for real numbers given as a stream of signed digits can be extracted from an appropriate formal proof.
Helmut Schwichtenberg +1 more
doaj +1 more source
A new coinductive confluence proof for infinitary lambda calculus [PDF]
Logical Methods in Computer Science, 2020 We present a new and formal coinductive proof of confluence and normalisation of B\"ohm reduction in infinitary lambda calculus. The proof is simpler than previous proofs of this result.
Łukasz Czajka
doaj +1 more source
Interfacing Automatic Proof Agents in Atelier B: Introducing "iapa" [PDF]
Electronic Proceedings in Theoretical Computer Science, 2017 The application of automatic theorem provers to discharge proof obligations is necessary to apply formal methods in an efficient manner. Tools supporting formal methods, such as Atelier~B, generate proof obligations fully automatically.
Lilian Burdy +2 more
doaj +1 more source
Unsealing the secrets of blockchain consensus: A systematic comparison of the formal security of proof-of-work and proof-of-stake [PDF]
ACM Symposium on Applied ComputingWith the increasing adoption of decentralized information systems based on a variety of permissionless blockchain networks, the choice of consensus mechanism is at the core of many controversial discussions.
Iván Abellán Álvarez +2 more
semanticscholar +1 more source