trees

12/5/20

Skills to be acquired in this tutorial:

To become familiar with the rules for propositional truth trees.

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

Conjunction

Tree Tutorial 1 Propositional Logic Truth Trees: Introduction

8/12/26

Graph theory and trees

'Trees' are a type of structure within the mathematical theory of graphs.

Some logicians write Rabc to mean the application of the predicate R to the terms a,b, and c. Others write R(a,b,c). We prefer the latter. The Colin Howson book uses a notation like R(a,b,c) for the application of a predicate R to the arguments or terms a, b, c. It employs the upper case letters A-Z, perhaps followed by subscripts, to be predicates, so, for example, R, S₁, T₁₂  are all predicates. The software supports this.

8/12/2026

Welcome!

1/29/08 10Software Under construction

Skills to be acquired in this tutorial:

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

Tutorial:

It is possible to use trees with formulas containing identity. Two new rules are needed.

5/26/09 10Software

Reading

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

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

Tree Quiz 1.

2/3/08 10 Software

Quiz 1 Applet

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

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.

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

∀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.