howson

2013

You need to know some propositional logic to be able to understand the tutorials to come. In particular, you need to know about the symbols used in propositional logic, truth tables, satisfiability, consistency, and semantic invalidity (by counter example). You do not need to know propositional rules of inference and derivations.

Howson [1997] will give you enough background.

Alternatively you could look at the first five propositional tutorials in Easy Deriver

2013

Reading

Colin Howson, [1997] Logic with trees Chapter 2

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.

2013

Skills to be acquired in this tutorial:

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

Reading

Colin Howson, [1997] Logic with trees Chapter 9

Tutorial:

It is possible to use trees with formulas containing identity. Really there are two different ways to implement it: either there are two new rules, or there is one new rule and a new way of closing a branch from a single formula. Both will be described.

2/3/08 10 Software The Widget for this has yet to be written. 2013

Quiz 2 Applet

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

 

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2013

Skills to be acquired in this tutorial:

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

Reading

Colin Howson, [1997] Logic with trees Chapter 6

Tutorial:

Introduction

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

Tree Quiz 1.

2/3/08 10 Software. The Widget for this has yet to be written. 2013

However, the Tree Quiz can be done in the web application. Launch the web application from here Deriver [Howson] — username 'logic' password 'logic'.

Preferences

You will need the relevant Preferences for this.

• Set gamesMenu to true; and  you can check that the parser is set to Howson.

 

2013

Reading

Colin Howson, [1997] Logic with trees Chapter 2

Exercises

Howson [1997] has a number of exercises. Many of them you will be able to do in the Widget below.

You can also try material of your own.

Here are a few hints

2013

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

Colin Howson, [1997] Logic with trees Chapter 2

Tutorial:

Closure and completeness

In Tutorial 1, we met the notions of closed and open branches (a closed branch was one containing a formula and also the negation of that formula, an open branch was a branch that was not closed).

Beginning Trees

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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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