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Single Idea 10163

[filed under theme 4. Formal Logic / D. Modal Logic ML / 1. Modal Logic ]

Full Idea

At the age of 19 Saul Kripke published a completeness proof of propositional modal logic.

Gist of Idea

Propositional modal logic has been proved to be complete

Source

report of Saul A. Kripke (A Completeness Theorem in Modal Logic [1959]) by Feferman / Feferman - Alfred Tarski: life and logic Int V

Book Ref

Feferman,S/Feferman,A.B.: 'Alfred Tarski: life and logic' [CUP 2008], p.286

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The 4 ideas from 'A Completeness Theorem in Modal Logic'

10760

With possible worlds, S4 and S5 are sound and complete, but S1-S3 are not even sound [Kripke, by Rossberg]

10163

Propositional modal logic has been proved to be complete [Kripke, by Feferman/Feferman]

16189

The variable domain approach to quantified modal logic invalidates the Barcan Formula [Kripke, by Simchen]

15132

The Barcan formulas fail in models with varying domains [Kripke, by Williamson]