Questions tagged [truth-tree]

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4 votes
1 answer
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How to generate counterexamples for modal logic trees from Girle

I am having a heck of a time understanding a counterexample discussion in Girle 2000. Here is the tree: But then, on p. 40, Girle reads off the tree: I understand where the values in k and l come ...
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1 vote
0 answers
59 views

Some Questions About A Truth Tree

The logical system used in this post is first-order logic. I’ve been reading Introduction to Logic: Predicate Logic, 2nd edition by Howard Pospesel, and I have some questions concerning a truth tree. ...
2 votes
1 answer
491 views

Proof Tree to Fitch Proof

I was wondering if anyone could help me on a proof I've been working on: I was able to check that it is valid with a proof tree generator (prooftools): However, I still haven't figured out the proof....
1 vote
0 answers
60 views

Prove that if the tree method determines that a set of sentences T implies a sentence A, then T does in fact imply A

Having trouble wrapping my head around how to prove this. My first question about this is what it means for the tree method to determine that the set of sentences implies A. I'm taking it to mean that ...
  • 19
2 votes
1 answer
431 views

How does a truth tree provide positive and negative effect tests for implication?

I'm trying to prove that the truth-tree method can be used to give a positive effect test for implication, and a negative effect test for non-implication. I've been given the fact that The truth-tree ...
2 votes
1 answer
153 views

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 ...
  • 19.1k
1 vote
1 answer
365 views

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: ...
  • 19.1k
0 votes
1 answer
300 views

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 ...
  • 19.1k
2 votes
2 answers
266 views

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 ...
  • 19.1k