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https://github.com/coq-community/comp-dec-modal
Completeness and Decidability of Modal Logic Calculi [maintainer=@chdoc]
https://github.com/coq-community/comp-dec-modal
coq ctl mathcomp modal-logics pdl
Last synced: about 2 months ago
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Completeness and Decidability of Modal Logic Calculi [maintainer=@chdoc]
- Host: GitHub
- URL: https://github.com/coq-community/comp-dec-modal
- Owner: coq-community
- License: other
- Created: 2020-09-07T15:37:29.000Z (over 4 years ago)
- Default Branch: master
- Last Pushed: 2024-08-11T14:44:54.000Z (5 months ago)
- Last Synced: 2024-08-11T16:00:16.466Z (5 months ago)
- Topics: coq, ctl, mathcomp, modal-logics, pdl
- Language: Coq
- Homepage: https://coq-community.org/comp-dec-modal/
- Size: 749 KB
- Stars: 8
- Watchers: 3
- Forks: 2
- Open Issues: 1
-
Metadata Files:
- Readme: README.md
- License: LICENSE
Awesome Lists containing this project
README
# Completeness and Decidability of Modal Logic Calculi
[![Docker CI][docker-action-shield]][docker-action-link]
[![Contributing][contributing-shield]][contributing-link]
[![Code of Conduct][conduct-shield]][conduct-link]
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[![DOI][doi-shield]][doi-link]
[docker-action-shield]: https://github.com/coq-community/comp-dec-modal/actions/workflows/docker-action.yml/badge.svg?branch=master
[docker-action-link]: https://github.com/coq-community/comp-dec-modal/actions/workflows/docker-action.yml
[contributing-shield]: https://img.shields.io/badge/contributions-welcome-%23f7931e.svg
[contributing-link]: https://github.com/coq-community/manifesto/blob/master/CONTRIBUTING.md
[conduct-shield]: https://img.shields.io/badge/%E2%9D%A4-code%20of%20conduct-%23f15a24.svg
[conduct-link]: https://github.com/coq-community/manifesto/blob/master/CODE_OF_CONDUCT.md
[zulip-shield]: https://img.shields.io/badge/chat-on%20zulip-%23c1272d.svg
[zulip-link]: https://coq.zulipchat.com/#narrow/stream/237663-coq-community-devs.20.26.20users
[coqdoc-shield]: https://img.shields.io/badge/docs-coqdoc-blue.svg
[coqdoc-link]: https://coq-community.org/comp-dec-modal/docs/latest/coqdoc/toc.html
[doi-shield]: https://zenodo.org/badge/DOI/10.22028/D291-26649.svg
[doi-link]: https://doi.org/10.22028/D291-26649
This project presents machine-checked constructive proofs of
soundness, completeness, decidability, and the small-model property
for the logics K, K*, CTL, and PDL (with and without converse).
For all considered logics, we prove soundness and completeness of
their respective Hilbert-style axiomatization. For K, K*, and CTL,
we also prove soundness and completeness for Gentzen systems (i.e.,
sequent calculi).
For each logic, the central construction is a pruning-based
algorithm computing for a given formula either a satisfying model of
bounded size or a proof of its negation. The completeness and
decidability results then follow with soundness from the existence
of said algorithm.
## Meta
- Author(s):
- Christian Doczkal (initial)
- Coq-community maintainer(s):
- Christian Doczkal ([**@chdoc**](https://github.com/chdoc))
- License: [CeCILL-B](LICENSE)
- Compatible Coq versions: 8.16 or later
- Additional dependencies:
- [MathComp](https://math-comp.github.io) 2.0 or later (`ssreflect` suffices)
- [Hierarchy Builder](https://github.com/math-comp/hierarchy-builder) 1.6.0 or later
- Coq namespace: `CompDecModal`
- Related publication(s):
- [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)
- [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)
## Building and installation instructions
The easiest way to install the latest released version of Completeness and Decidability of Modal Logic Calculi
is via [OPAM](https://opam.ocaml.org/doc/Install.html):
```shell
opam repo add coq-released https://coq.inria.fr/opam/released
opam install coq-comp-dec-modal
```
To instead build and install manually, do:
``` shell
git clone https://github.com/coq-community/comp-dec-modal.git
cd comp-dec-modal
make # or make -j
make install
```
## Documentation
The developments for the individual logics are described in the
publications listed above. The developments on K, K*, and CTL are
described in the author's PhD thesis titled "A Machine-Checked
Constructive Metatheory of Computation Tree Logic". The developments
on PDL and PDL with converse are described in the CPP'18 paper.
### Structure
- The directory `libs` contains infrastructure shared between the
developments. This includes:
- `fset.v`: a library for finite sets over types with a choice operator (a precursor of [finmap](https://github.com/math-comp/finmap)).
- `fset_tac.v`: rudimentary automation for the above (originally implemented by [Alexander Anisimov](https://www.ps.uni-saarland.de/~anisimov/bachelor.php)).
- `modular_hilbert.v`: a library for constructing proofs in Hilbert axiomatizations for modal logics.
- `sltype.v`: generic lemmas for alpha/beta decomposition of modal-logic formulas.
- the remaining directories contain the formalizations for the respective logics.