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Questions tagged [truth-tree]

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If I cannot draw a world in a truth tree in modal logic does that mean that no other worlds exist for that statement?

Suppose I have a truth tree for a modal logic statement that is closed or is open but for which I cannot continue drawing worlds, does that mean that there are no other accessible worlds in that modal ...
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What is the counterexample in modal system K for “⬜A ➡A”?

As I understand it from Modal Logic 2.1 - the systems M, B, S4 & S5, I should not be able to show "⬜A ➡A" in modal logic K. The following truth tree seems to confirm this, if I did it correctly: ...
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Why can one not draw a world in modal logic given necessity?

In Modal Logic 1.2 -- truth trees for K about 1:30 into the video, the presenter said: If you have possibly A then you need to draw an arrow to a new world and derive A in that world because w0 ...
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What is the justification for closing a whole branch in a modal truth tree diagram if there is a contradiction in only one world?

I am watching "Modal logic 1.2 - truth trees for system K" presented through Kane B's channel. The standard propositional truth tree diagrams are not a problem. Where I am having trouble is opening ...