Matches in SemOpenAlex for { <https://semopenalex.org/work/W4233344990> ?p ?o ?g. }
Showing items 1 to 67 of
67
with 100 items per page.
- W4233344990 abstract "Suppose I say “Here is a machine-checked proof of Fermat's last theorem (FLT)”. How can you use my putative machine-checked proof as evidence for belief in FLT? I start from the position that you must have some personal experience of understanding to attain belief, and to have this experience you must engage your intuition and other mental processes which are impossible to formalise. By machine-checked proof I mean a formal derivation in some given formal system; I am talking about derivability, not about truth. Further, I want to talk about actually believing an actual formal proof, not about formal proofs in principle; to be interesting, any approach to this problem must be feasible. You might try to read my proof, just as you would a proof in a journal; however, with the current state of the art, this proof will surely be too long for you to have confidence that you have understood it. This paper presents a technological approach for reducing the problem of believing a formal proof to the same psychological and philosophical issues as believing a conventional proof in a mathematics journal. The approach is not entirely successful philosophically as there seems to be a fundamental difference between machine-checked mathematics, which depends on empirical knowledge about the physical world, and informal mathematics, which needs no such knowledge (see section 3.2.2). In the rest of this introduction I outline the approach and mention related work. In following sections I discuss what we expect from a proof, add details to the approach, pointing out problems that arise, and concentrate on what I believe is the primary technical problem: expressiveness and feasibility for checking of formal systems and representations of mathematical notions. The problem is how to believe FLT when given only a putative proof formalised in a given logic. Assume it is a logic that you believe is consistent, and appropriate for FLT. The “thing” I give you is some computer files. There may be questions about the physical and abstract representations of the files (how to read them physically and how to parse them as a proof), and correctness of the hardware and software to do these things; ignore them until section 3.1." @default.
- W4233344990 created "2022-05-12" @default.
- W4233344990 creator A5069354082 @default.
- W4233344990 date "1998-10-15" @default.
- W4233344990 modified "2023-10-17" @default.
- W4233344990 title "How to believe a machine-checked proof" @default.
- W4233344990 doi "https://doi.org/10.1093/oso/9780198501275.003.0013" @default.
- W4233344990 hasPublicationYear "1998" @default.
- W4233344990 type Work @default.
- W4233344990 citedByCount "1" @default.
- W4233344990 countsByYear W42333449902012 @default.
- W4233344990 crossrefType "book-chapter" @default.
- W4233344990 hasAuthorship W4233344990A5069354082 @default.
- W4233344990 hasConcept C105605280 @default.
- W4233344990 hasConcept C108710211 @default.
- W4233344990 hasConcept C111472728 @default.
- W4233344990 hasConcept C118615104 @default.
- W4233344990 hasConcept C132010649 @default.
- W4233344990 hasConcept C138885662 @default.
- W4233344990 hasConcept C154945302 @default.
- W4233344990 hasConcept C173613240 @default.
- W4233344990 hasConcept C195653647 @default.
- W4233344990 hasConcept C199343813 @default.
- W4233344990 hasConcept C203265346 @default.
- W4233344990 hasConcept C2318724 @default.
- W4233344990 hasConcept C2524010 @default.
- W4233344990 hasConcept C2777686260 @default.
- W4233344990 hasConcept C33923547 @default.
- W4233344990 hasConcept C41008148 @default.
- W4233344990 hasConcept C71924100 @default.
- W4233344990 hasConcept C87670640 @default.
- W4233344990 hasConcept C94461902 @default.
- W4233344990 hasConceptScore W4233344990C105605280 @default.
- W4233344990 hasConceptScore W4233344990C108710211 @default.
- W4233344990 hasConceptScore W4233344990C111472728 @default.
- W4233344990 hasConceptScore W4233344990C118615104 @default.
- W4233344990 hasConceptScore W4233344990C132010649 @default.
- W4233344990 hasConceptScore W4233344990C138885662 @default.
- W4233344990 hasConceptScore W4233344990C154945302 @default.
- W4233344990 hasConceptScore W4233344990C173613240 @default.
- W4233344990 hasConceptScore W4233344990C195653647 @default.
- W4233344990 hasConceptScore W4233344990C199343813 @default.
- W4233344990 hasConceptScore W4233344990C203265346 @default.
- W4233344990 hasConceptScore W4233344990C2318724 @default.
- W4233344990 hasConceptScore W4233344990C2524010 @default.
- W4233344990 hasConceptScore W4233344990C2777686260 @default.
- W4233344990 hasConceptScore W4233344990C33923547 @default.
- W4233344990 hasConceptScore W4233344990C41008148 @default.
- W4233344990 hasConceptScore W4233344990C71924100 @default.
- W4233344990 hasConceptScore W4233344990C87670640 @default.
- W4233344990 hasConceptScore W4233344990C94461902 @default.
- W4233344990 hasLocation W42333449901 @default.
- W4233344990 hasOpenAccess W4233344990 @default.
- W4233344990 hasPrimaryLocation W42333449901 @default.
- W4233344990 hasRelatedWork W1524804222 @default.
- W4233344990 hasRelatedWork W1561664087 @default.
- W4233344990 hasRelatedWork W1854197585 @default.
- W4233344990 hasRelatedWork W2131024625 @default.
- W4233344990 hasRelatedWork W2463991046 @default.
- W4233344990 hasRelatedWork W2755232768 @default.
- W4233344990 hasRelatedWork W2795365301 @default.
- W4233344990 hasRelatedWork W4233344990 @default.
- W4233344990 hasRelatedWork W2119682046 @default.
- W4233344990 hasRelatedWork W2491370528 @default.
- W4233344990 isParatext "false" @default.
- W4233344990 isRetracted "false" @default.
- W4233344990 workType "book-chapter" @default.