trees

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

The Modal Negation (MN) rules

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Reading

M.Bergmann, J.Moor, J.Nelson, [2008] The Logic Book Chapter 4

Exercises

Bergmann [2008] has a number of exercises. Many of them you will be able to do in the Applet below.

Here are a few hints

1/25/09

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.]

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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 applet will let you try a few.

Review of Sentential Tree Rules

5/18/09

5/18/09 10 Software Under construction

Skills to be acquired in this tutorial:

To become familiar with the notions of closed and complete trees. To be able to use trees to test for satisfiability and invalidity.

Reading

M.Bergmann, J.Moor, J.Nelson, [2004] The Logic Book Chapter 4

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Skills to be acquired in this tutorial:

To become familiar with the rules for sentential truth trees.

Reading

M.Bergmann, J.Moor, J.Nelson, [2004] The Logic Book Chapter 4

Tutorial:

Truth Tree Rules

Trees are going to be used to 'picture' the truth conditions or requirements for a formula (then, as the technique is developed, for several formulas at once).

Any easy way to remember the rules is to regard them as having been built from the truth tables.

The truth table for 'and' is

Beginning Trees

2/10/08

A Simple Tree

[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.]

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Prerequisities

You need to know some sentential logic to be able to understand this. In particular, you need to know about the symbols used in sentential logic, truth tables, satisfiability, consistency, and semantic invalidity (by counter example). You do not need to know sentential rules of inference and derivations. [The tutorials on sentential logic elsewhere on this site give the required background. Alternatively

M.Bergmann, J.Moor, J.Nelson, [2008] The Logic Book Chapter 4

[The material on Trees under Howson is probably more current than this. If you'd like me to update these Tree Notes, send me an email mfricke@SoftOption.Us .]

This section of the tutorials and

M.Bergmann, J.Moor, J.Nelson [2008], The Logic Book [the current edition is the 5th edition]

would work well together.