Combining Texts
Ideas for
'The Really Hard Problem', 'A Completeness Theorem in Modal Logic' and 'A Theory of Universals'
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5 ideas
4. Formal Logic / D. Modal Logic ML / 1. Modal Logic
10163
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Propositional modal logic has been proved to be complete [Kripke, by Feferman/Feferman]
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4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / a. Systems of modal logic
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With possible worlds, S4 and S5 are sound and complete, but S1-S3 are not even sound [Kripke, by Rossberg]
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4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / g. System S4
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If what is actual might have been impossible, we need S4 modal logic [Armstrong, by Lewis]
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4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula
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The variable domain approach to quantified modal logic invalidates the Barcan Formula [Kripke, by Simchen]
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The Barcan formulas fail in models with varying domains [Kripke, by Williamson]
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