trees

Tree Tutorial 2 More Rules

10/20/26

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.

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.

For example, the truth table for 'and' is

Conjunction

8/15/26

Roll your own

• You have to use the right (unicode/html) logical symbols. Check Writing symbols

• The symbols in use here are ~ & ∨ →  

  ≡

There are the ordinary (non-modal) tree propositional rules plus

The Modal Negation (MN) rules

5/30/12

Skills to be acquired in this tutorial:

To learn about the Uniqueness quantifier (a part of identity), and to be introduced to definite descriptions.

Why this is useful:

Uniqueness is central in mathematics, and definite descriptions is a core area in philosophical logic.

8/10/2026

It has become a challenge to run the legacy Deriver application, which was written in Java Swing, simply because few Users have Java on their computers. Fortunately, Leaning Technologies have devised some technology, CheerpJ, that allow Java Swing applications to run in a web browser. 

8/12/26

Reading

Colin Howson, [1997] Logic with trees Chapter 12 Section 2

The Howson [1997] does not expand on modal logic (and modal trees) so a text like

Rod Girle [2000] Modal Logics and Philosophy

would definitely be a help here.

Tutorial

[Modal logic is a vast area, what is being presented here is the briefest of glimpses through the shop window (a book like the Girle would help you go further).]

Exercise: Finding a counter-example.