trees

8/15/26

Roll your own

• You have to use the right (unicode/html) logical symbols. Check Writing symbols

• The symbols in use here are ~ & ∨ →  

  ≡

There are the ordinary (non-modal) tree propositional rules plus

The Modal Negation (MN) rules

 

5/30/12

Skills to be acquired in this tutorial:

To learn about the Uniqueness quantifier (a part of identity), and to be introduced to definite descriptions.

Why this is useful:

Uniqueness is central in mathematics, and definite descriptions is a core area in philosophical logic.

8/10/2026

It has become a challenge to run the legacy Deriver application, which was written in Java Swing, simply because few Users have Java on their computers. Fortunately, Leaning Technologies have devised some technology, CheerpJ, that allow Java Swing applications to run in a web browser. 

 

 

8/12/26

Reading

Colin Howson, [1997] Logic with trees Chapter 12 Section 2

The Howson [1997] does not expand on modal logic (and modal trees) so a text like

Rod Girle [2000] Modal Logics and Philosophy

would definitely be a help here.

Tutorial

[Modal logic is a vast area, what is being presented here is the briefest of glimpses through the shop window (a book like the Girle would help you go further).]

 

Exercise: Finding a counter-example.

2013

Reading a counter example from an open branch

[This is a Quicktime Movie, click the Play button to view it. The logical symbols you see in use may be different to the ones you are familiar with (sorry about that, but it is not practical to produce different movies for all the minor variations in symbols). Any differences will not affect the principles being explained here.]

2013

An example of the tree widget in use (and we are showing a different parser here to the earlier ones)

The logical symbols in use are ¬ ∧ ∨ → ↔ ∀ ∃ .

Determine whether these arguments are valid (ie try to produce closed trees for them)

a) ∀x(F(x)→G(x)), ∃x¬G(x) ∴ ∃x¬F(x)
b) ∀x(F(x)→∀yG(y)), F(a) ∴ ∀xG(x)
c) ∀x(A(x)→B(x)), ∀x(¬A(x)→C(x))∴ ∀x(¬B(x)→¬C(x))
d) ∃xF(x),∀x(¬G(x)→¬F(x)),∀xM(x) ∴ ∃xG(x)∧∃xM(x)

Last altered 6/20/12

A central use for Trees is to produce a counter example to an invalid argument. To do this, you construct a tree with a complete open branch. You will be able to do this for invalid arguments (but not valid ones). Then you run up that branch assigning all atomic formulas True and all negations of atomic formulas False.

 

This software will let you try a few.

 

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Exercise: Finding a counter-example.