trees

8/15/2016

Skills to be acquired in this tutorial:

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

Tutorial:

Introduction

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

8/12/26

You can try material of your own below.

Here are a few hints

8/12/26

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.

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).

5/28/12

A Simple Tree

[This is a Video, click the Play button to view it..]

8/15/26

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