hausman

1/23/09 10 Software

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.

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∃D. The constant, a, must be new to the branch [here the computer will choose for you]

 

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∀D. Any closed term, stage 1, your choice

∀D. Any closed term, stage 2, a chosen

2/3/08 10 Software

Quiz 2 Applet

Your browser is not displaying the Deriver applet. Try downloading Deriver itself by clicking on the link elsewhere on the page.

 

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.