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meta.yml
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---
fullname: Completeness and Decidability of Modal Logic Calculi
shortname: comp-dec-modal
organization: coq-community
community: true
action: true
coqdoc: true
doi: 10.22028/D291-26649
synopsis: >-
Constructive proofs of soundness and completeness for K, K*, CTL,
PDL, and PDL with converse
description: |-
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.
publications:
- pub_title: A Machine-Checked Constructive Metatheory of Computation Tree Logic
pub_url: https://www.ps.uni-saarland.de/static/doczkal-diss/index.php
pub_doi: 10.22028/D291-26649
- pub_title: Completeness and decidability of converse PDL in the constructive type theory of Coq
pub_url: https://hal.archives-ouvertes.fr/hal-01646782/
pub_doi: 10.1145/3167088
authors:
- name: Christian Doczkal
initial: true
maintainers:
- name: Christian Doczkal
nickname: chdoc
opam-file-maintainer: [email protected]
opam-file-version: dev
license:
fullname: CeCILL-B
identifier: CECILL-B
supported_coq_versions:
text: 8.16 or later
opam: '{>= "8.16"}'
tested_coq_opam_versions:
- version: 'coq-dev'
repo: 'mathcomp/mathcomp-dev'
- version: '2.2.0-coq-8.19'
repo: 'mathcomp/mathcomp'
- version: '2.2.0-coq-8.18'
repo: 'mathcomp/mathcomp'
- version: '2.2.0-coq-8.17'
repo: 'mathcomp/mathcomp'
- version: '2.2.0-coq-8.16'
repo: 'mathcomp/mathcomp'
- version: '2.1.0-coq-8.17'
repo: 'mathcomp/mathcomp'
- version: '2.1.0-coq-8.16'
repo: 'mathcomp/mathcomp'
- version: '2.0.0-coq-8.17'
repo: 'mathcomp/mathcomp'
- version: '2.0.0-coq-8.16'
repo: 'mathcomp/mathcomp'
# “At 01:42 on Sunday.”
ci_cron_schedule: '42 1 * * 0'
dependencies:
- opam:
name: coq-mathcomp-ssreflect
version: '{>= "2.0"}'
description: |-
[MathComp](https://math-comp.github.io) 2.0 or later (`ssreflect` suffices)
- opam:
name: coq-hierarchy-builder
version: '{>= "1.6.0"}'
description: |-
[Hierarchy Builder](https://github.com/math-comp/hierarchy-builder) 1.6.0 or later
namespace: CompDecModal
keywords:
- name: modal logic
- name: completeness
- name: decidability
- name: Hilbert system
- name: computation tree logic
- name: propositional dynamic logic
categories:
- name: Mathematics/Logic/Modal logic
coqdoc_index: "docs/latest/coqdoc/toc.html"
documentation: |-
## 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.
---