{"id":27214582,"url":"https://github.com/rocq-community/comp-dec-modal","last_synced_at":"2025-08-25T21:04:03.273Z","repository":{"id":44885155,"uuid":"293567285","full_name":"rocq-community/comp-dec-modal","owner":"rocq-community","description":"Completeness and Decidability of Modal Logic Calculi 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file was generated from `meta.yml`, please do not edit manually.\nFollow the instructions on https://github.com/coq-community/templates to regenerate.\n---\u003e\n# Completeness and Decidability of Modal Logic Calculi\n\n[![Docker CI][docker-action-shield]][docker-action-link]\n[![Contributing][contributing-shield]][contributing-link]\n[![Code of Conduct][conduct-shield]][conduct-link]\n[![Zulip][zulip-shield]][zulip-link]\n[![coqdoc][coqdoc-shield]][coqdoc-link]\n[![DOI][doi-shield]][doi-link]\n\n[docker-action-shield]: https://github.com/coq-community/comp-dec-modal/actions/workflows/docker-action.yml/badge.svg?branch=master\n[docker-action-link]: https://github.com/coq-community/comp-dec-modal/actions/workflows/docker-action.yml\n\n[contributing-shield]: https://img.shields.io/badge/contributions-welcome-%23f7931e.svg\n[contributing-link]: https://github.com/coq-community/manifesto/blob/master/CONTRIBUTING.md\n\n[conduct-shield]: https://img.shields.io/badge/%E2%9D%A4-code%20of%20conduct-%23f15a24.svg\n[conduct-link]: https://github.com/coq-community/manifesto/blob/master/CODE_OF_CONDUCT.md\n\n[zulip-shield]: https://img.shields.io/badge/chat-on%20zulip-%23c1272d.svg\n[zulip-link]: https://coq.zulipchat.com/#narrow/stream/237663-coq-community-devs.20.26.20users\n\n[coqdoc-shield]: https://img.shields.io/badge/docs-coqdoc-blue.svg\n[coqdoc-link]: https://coq-community.org/comp-dec-modal/docs/latest/coqdoc/toc.html\n\n[doi-shield]: https://zenodo.org/badge/DOI/10.22028/D291-26649.svg\n[doi-link]: https://doi.org/10.22028/D291-26649\n\nThis project presents machine-checked constructive proofs of\nsoundness, completeness, decidability, and the small-model property\nfor the logics K, K*, CTL, and PDL (with and without converse).\n\nFor all considered logics, we prove soundness and completeness of\ntheir respective Hilbert-style axiomatization. For K, K*, and CTL,\nwe also prove soundness and completeness for Gentzen systems (i.e.,\nsequent calculi).\n\nFor each logic, the central construction is a pruning-based\nalgorithm computing for a given formula either a satisfying model of\nbounded size or a proof of its negation. The completeness and\ndecidability results then follow with soundness from the existence\nof said algorithm.\n  \n\n## Meta\n\n- Author(s):\n  - Christian Doczkal (initial)\n- Coq-community maintainer(s):\n  - Christian Doczkal ([**@chdoc**](https://github.com/chdoc))\n- License: [CeCILL-B](LICENSE)\n- Compatible Coq versions: 8.16 or later\n- Additional dependencies:\n  - [MathComp](https://math-comp.github.io) 2.0 or later (`ssreflect` suffices)\n  - [Hierarchy Builder](https://github.com/math-comp/hierarchy-builder) 1.6.0 or later\n- Coq namespace: `CompDecModal`\n- Related publication(s):\n  - [A Machine-Checked Constructive Metatheory of Computation Tree Logic](https://www.ps.uni-saarland.de/static/doczkal-diss/index.php) doi:[10.22028/D291-26649](https://doi.org/10.22028/D291-26649)\n  - [Completeness and decidability of converse PDL in the constructive type theory of Coq](https://hal.archives-ouvertes.fr/hal-01646782/) doi:[10.1145/3167088](https://doi.org/10.1145/3167088)\n\n## Building and installation instructions\n\nThe easiest way to install the latest released version of Completeness and Decidability of Modal Logic Calculi\nis via [OPAM](https://opam.ocaml.org/doc/Install.html):\n\n```shell\nopam repo add coq-released https://coq.inria.fr/opam/released\nopam install coq-comp-dec-modal\n```\n\nTo instead build and install manually, do:\n\n``` shell\ngit clone https://github.com/coq-community/comp-dec-modal.git\ncd comp-dec-modal\nmake   # or make -j \u003cnumber-of-cores-on-your-machine\u003e \nmake install\n```\n\n\n## Documentation\n\nThe developments for the individual logics are described in the\npublications listed above. The developments on K, K*, and CTL are\ndescribed in the author's PhD thesis titled \"A Machine-Checked\nConstructive Metatheory of Computation Tree Logic\". The developments\non PDL and PDL with converse are described in the CPP'18 paper.\n\n### Structure\n\n- The directory `libs` contains infrastructure shared between the\n  developments. This includes:\n  - `fset.v`: a library for finite sets over types with a choice operator (a precursor of [finmap](https://github.com/math-comp/finmap)).\n  - `fset_tac.v`: rudimentary automation for the above (originally implemented by [Alexander Anisimov](https://www.ps.uni-saarland.de/~anisimov/bachelor.php)).\n  - `modular_hilbert.v`: a library for constructing proofs in Hilbert axiomatizations for modal logics.\n  - `sltype.v`: generic lemmas for alpha/beta decomposition of modal-logic formulas.\n- the remaining directories contain the formalizations for the respective logics.\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Frocq-community%2Fcomp-dec-modal","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Frocq-community%2Fcomp-dec-modal","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Frocq-community%2Fcomp-dec-modal/lists"}