Skip to content
New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

feat(Normal Modal): Strength of Logics Part.1 #23

Merged
merged 15 commits into from
Mar 21, 2024

Conversation

SnO2WMaN
Copy link
Collaborator

@SnO2WMaN SnO2WMaN commented Feb 8, 2024

TODO

  • Strong Soundness: Γ ⊢ᴹ[Λ]! p → Γ ⊨ᴹ[(𝔽(Λ) : FrameClass β)] p
  • Consequence Weakening: (h : Λ₁ ⪯ᴸ Λ₂): Γ ⊨ᴹ[(𝔽(Λ₂) : FrameClass α)] p → Γ ⊨ᴹ[(𝔽(Λ₁) : FrameClass α)] p
  • Property on strict logic stronger

Optional

CompletenessLogic.FrameClassDefinabilityの証明はAxiomSetに依らずほとんど同じなのでマクロなどを駆使して再利用できるようにしたい(さもなければmodal cubeの残りの論理に対して全く同じ証明を10個ほど書かなければならないため,コード量がただただかさむ)

@SnO2WMaN SnO2WMaN changed the title feat(Normal Modal): add modal cube feat(Normal Modal): Strength of Logics Feb 10, 2024
@SnO2WMaN SnO2WMaN changed the title feat(Normal Modal): Strength of Logics feat(Normal Modal): Strength of Logics Part.1 Mar 21, 2024
@SnO2WMaN
Copy link
Collaborator Author

SnO2WMaN commented Mar 21, 2024

あまりにもコミットが積み上がったので一旦これでPRとしては完了したものとしてreadyにする.示したものは以下.

  • 𝐒𝟒 <ᴸ 𝐒𝟓: 𝐒𝟓𝐒𝟒より真に強い
  • 𝐒𝟓 =ᴸ 𝐊𝐓𝟒𝐁: 𝐒𝟓𝐊𝐓𝟒𝐁と同程度の強さ
  • 強健全性定理: Γ ⊢ᴹ[Λ]! p → Γ ⊨ᴹ[(𝔽(Λ) : FrameClass β)] p

@SnO2WMaN SnO2WMaN marked this pull request as ready for review March 21, 2024 11:00
Logic/Logic/HilbertStyle2.lean Outdated Show resolved Hide resolved
Logic/Modal/Normal/Deduction.lean Outdated Show resolved Hide resolved
Logic/Modal/Normal/HilbertStyle.lean Outdated Show resolved Hide resolved
Logic/Modal/Normal/Formula.lean Outdated Show resolved Hide resolved
Logic/Modal/Normal/HilbertStyle.lean Outdated Show resolved Hide resolved
@SnO2WMaN
Copy link
Collaborator Author

rebaseして現行の修正分に合わせた.

@iehality
Copy link
Owner

Logic/HilbertStyle.leanを削除しLogic/HilbertStyle2.leanはLogic/Deduction.leanに改名しました。また命題直感主義論理の証明体系をSystemのインスタンスとして定義し直していますが、Systemの根幹部分をDeductionと融合させたので本質的な問題はないはずです(突然大規模な変更を加えてしまってすみません)。これは問題はなさそうなのでマージします。

@iehality iehality merged commit c3911b1 into iehality:master Mar 21, 2024
1 check passed
@SnO2WMaN SnO2WMaN deleted the modalcube branch March 21, 2024 19:11
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment
Labels
None yet
Projects
None yet
Development

Successfully merging this pull request may close these issues.

None yet

2 participants