hausman

1/29/08

Skills to be acquired in this tutorial:

To become familiar with the new rules for predicate logic trees.

Reading

A. Hausman, H.Kahane, P.Tidman, [2007] Logic and Philosophy Chapter 12

Tutorial:

Introduction

There are further rules for predicate logic trees (which we will come to shortly).

1/27/08 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

A. Hausman, H.Kahane, P.Tidman, [2007] Logic and Philosophy Chapter 6

5/26/09 10Software

Reading

A. Hausman, H.Kahane, P.Tidman, [2007] Logic and Philosophy Chapter 6

Exercises

Hausman [2007] has a number of exercises. Many of them you will be able to do in the Applet below.

Here are a few hints

Review of Sentential Tree Rules

5/18/09

1/26/08 10Software

Skills to be acquired in this tutorial:

To become familiar with the rules for sentential truth trees.

Reading

A. Hausman, H.Kahane, P.Tidman, [2007] Logic and Philosophy Chapter 6

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

1/27/08 10Software

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 give the required background.]

Skills to be acquired in this tutorial:

To become familiar with the notions of tree, branch, open branch, closed branch.

[The material on Trees under Howson is probably more current than this. These notes will be updated, though (Nov 2011)]

This section of the tutorials and

A.Hausman, H.Kahane, P.Tidman [2007], Logic and Philosophy

would work well together.

Roll your own derivations

6/21/07 10 Software

You may have derivations of your own that you wish to try. Just type, paste, or drag and drop, them into the panel, select your derivation, and click 'Start from selection'. [Often copy-and-paste won't work directly from a Web Page; however, usually drag-and-drop will work!]

You will need to use the correct logical symbols. Here they are

F ∴ F & G ∼ & ∨ ⊃ ≡  ∃ ∴ (or use the palette to produce them)

2/5/08

The Rule of Universal Instantiation UI

If a derivation contains a line of the form

n (<variable>)<scope> <any justification>

then a line of the form

<<scope>[<term>/<variable>]> 'n UI'

may be added to the derivation, provided that <variable> is free for <term> in the <scope> ie that the substitution [<term>/<variable>] is legitimate .