{"id":13379248,"url":"https://github.com/FormalizedFormalLogic/Foundation","last_synced_at":"2025-03-13T05:30:43.593Z","repository":{"id":158668900,"uuid":"600521950","full_name":"FormalizedFormalLogic/Foundation","owner":"FormalizedFormalLogic","description":"Lean4 Logic Formalization","archived":false,"fork":false,"pushed_at":"2024-07-25T21:55:05.000Z","size":2201,"stargazers_count":49,"open_issues_count":13,"forks_count":4,"subscribers_count":5,"default_branch":"master","last_synced_at":"2024-07-25T23:28:12.305Z","etag":null,"topics":["incompleteness","lean4","logic"],"latest_commit_sha":null,"homepage":"https://iehality.github.io/lean4-logic/book/","language":"Lean","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":"apache-2.0","status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/FormalizedFormalLogic.png","metadata":{"files":{"readme":"README.md","changelog":null,"contributing":null,"funding":null,"license":"LICENSE","code_of_conduct":null,"threat_model":null,"audit":null,"citation":null,"codeowners":null,"security":null,"support":null,"governance":null,"roadmap":null,"authors":null,"dei":null,"publiccode":null,"codemeta":null}},"created_at":"2023-02-11T18:48:33.000Z","updated_at":"2024-07-25T23:28:17.784Z","dependencies_parsed_at":"2023-09-26T21:35:25.772Z","dependency_job_id":"35e214e4-cf99-4e63-b521-c8796161ead9","html_url":"https://github.com/FormalizedFormalLogic/Foundation","commit_stats":null,"previous_names":["formalizedformallogic/foundation"],"tags_count":0,"template":false,"template_full_name":null,"repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/FormalizedFormalLogic%2FFoundation","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/FormalizedFormalLogic%2FFoundation/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/FormalizedFormalLogic%2FFoundation/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/FormalizedFormalLogic%2FFoundation/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/FormalizedFormalLogic","download_url":"https://codeload.github.com/FormalizedFormalLogic/Foundation/tar.gz/refs/heads/master","host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":243350968,"owners_count":20276893,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2022-07-04T15:15:14.044Z","host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":["incompleteness","lean4","logic"],"created_at":"2024-07-30T07:01:45.404Z","updated_at":"2025-03-13T05:30:43.581Z","avatar_url":"https://github.com/FormalizedFormalLogic.png","language":"Lean","funding_links":[],"categories":["Lean"],"sub_categories":[],"readme":"[Book]: https://formalizedformallogic.github.io/Foundation/book\n[Doc]: https://FormalizedFormalLogic.github.io/Foundation/doc\n\n# Foundation\n\nFormalizing mathematical logics in Lean 4.\n\n## Summary\n\nMain Result in this repository. More results and details are in [Book] and [Doc].\n\n- [Propositional Logic][prop]\n  - [Tait-style calculus][prop:classical_tait] and [completeness][prop:classical_tait_complete]\n  - [Completeness for Kripke semantics][prop:kripke]\n  - [Disjunctive Property of intuitionistic logic][prop:int_disjunctive]\n  - Rejection Law of Excluded Middle in intuitionistic logic and [sublogic relations][prop:sublogics]\n- [First-Order Logic][first_order] and [Arithmetics][arith]\n  - [Completeness Theorem][first_order:completeness]\n  - [Gödel-Gentzen Translation][first_order:goedel_translation]\n  - [Cut-elimination of first-order sequent calculus _(Gentzen's Hauptsatz)_][first_order:haupstaz]\n  - [Arithmetic][arith] and [Arithmetization](arithmetization)\n  - Gödel's [First][arith:goedel_it1] and [Second][arith:goedel_it2] Incompleteness Theorems\n- [Basic Modal Logic][modal:logic] (with modal operators $\\Box, \\Diamond$)\n  - [Kripke completeness for well-known subsystems][modal:logic_kripke_completeness]\n  - [_Modal Cube_][modal:cube], and [sublogic relations for other logics](modal:sublogic)\n  - [Gödel-McKinsey-Tarski Theorem][modal:gmt_theorem] and [Modal Companions](modal:companion)\n  - [Provability Logic][provability_logic]\n\n[prop]: ./Foundation/Propositional\n[prop:classical_tait]: ./Foundation/Propositional/Tait/Calculus.lean\n[prop:classical_tait_complete]: ./Foundation/Propositional/Classical/Tait.lean\n[prop:classical_complete]: ./Foundation/Propositional/Classical/Tait.lean\n[prop:kripke]: ./Foundation/Propositional/Kripke\n[prop:int_disjunctive]: ./Foundation/Propositional/Kripke/Hilbert/Int.lean\n[prop:sublogics]: ./Foundation/Propositional/Logic/Sublogic.lean\n[first_order]: https://formalizedformallogic.github.io/Foundation/book/first_order/index.html\n[first_order:completeness]: https://formalizedformallogic.github.io/Foundation/book/first_order/completeness.html\n[first_order:haupstaz]: ./Foundation/FirstOrder/Hauptsatz.lean\n[first_order:goedel_translation]: ./Foundation/IntFO/Translation.lean\n[arith]: https://formalizedformallogic.github.io/Foundation/book/first_order/arithmetics.html\n[arithmetization]: ./Foundation/Arithmetization\n[arith:goedel_it1]: https://formalizedformallogic.github.io/Foundation/book/first_order/goedel1.html\n[arith:goedel_it2]: https://formalizedformallogic.github.io/Foundation/book/first_order/goedel2.html\n[modal:logic]: ./Foundation/Modal\n[modal:logic_kripke_completeness]: ./Foundation/Modal/Kripke/Hilbert\n[modal:cube]: ./Foundation/Modal/Logic/Sublogic/ModalCube.lean\n[modal:sublogic]: ./Foundation/Modal/Logic/Sublogic\n[modal:gmt_theorem]: ./Foundation/Modal/ModalCompanion/Int.lean\n[modal:companion]: ./Foundation/Modal/ModalCompanion\n[provability_logic]: ./Foundation/Incompleteness/ProvabilityLogic\n\n## Documents\n\n- [Book], summary of results.\n- [Doc], documentation generated by [doc-gen4](https://github.com/leanprover/doc-gen4).\n\n## Sponsor\n\nThis project is supported by [Proxima Technology].\n\n[\u003cimg height=\"60\" src=\"https://raw.githubusercontent.com/FormalizedFormalLogic/.github/refs/heads/main/profile/proxima_technology.svg\"\u003e][Proxima Technology]\n\n[Proxima Technology]: https://proxima-ai-tech.com/\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2FFormalizedFormalLogic%2FFoundation","html_url":"https://awesome.ecosyste.ms/projects/github.com%2FFormalizedFormalLogic%2FFoundation","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2FFormalizedFormalLogic%2FFoundation/lists"}