predicate

The Tutorial

A few concepts are needed give a simple portrayal of the truth and falsity of predicate logic formulas.

There is the notion of an Interpretation which consists of a Universe together with an account of how the various symbols in the predicate logic formulas apply in this Universe.

There should be a Universe, which is the collection of the objects that the formulas is about. We write, for example,

Universe = {a,b,c}

10/12/26

Skill to be acquired:

To learn how to interpret simple predicate logic formulas as being true or false.

Why this is useful:

This helps in proving invalidity by the technique of displaying a counter-example.

The Tutorial:

In propositional logic, we just took it that each of the atomic propositions either is true or is false-- we did not look into the structure of the propositions.

Truth can be discussed in more detail in predicate logic.

A start can be made in predicate logic by taking apart 'atomic' propositions and by re-phrasing what they have to say in a 'entity-has-property' way.

The constant terms a,b,c...h are used to denote entities, the predicates A,B,C...Z are used to denote properties that these entities have, and these are put together by writing the predicate first followed by the term, for example Gb.

Tutorial

In predicate logic, many different styles of expression in English get cast into the same 'property-is-had-by-entity' form. For example,

Beryl is wise. (ie adjective)

Beryl runs. (ie verb)

Beryl is a philosopher. (ie noun)

might be symbolized Wb, Rb, and Pb, respectively.

Skills to be acquired in this tutorial:

To start learning how to symbolize propositions using predicate logic.

The Tutorial:

There are many valid arguments which cannot be shown to be valid using propositional logic alone. For example,

Beryl is a philosopher.

All philosophers are wise.

Therefore

Beryl is wise.

Tutorials 11 to 25: predicate logic, using the Copi syntax.

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. 

Roll your own derivations

2013

You may have derivations of your own that you wish to try. Just type, paste, or drag and drop, them into the panel, select your derivation, and click 'Start from selection'. [Often copy-and-paste won't work directly from a Web Page; however, usually drag-and-drop will work!]

You will need to use the correct logical symbols. Here they are

F ∴ F & G ∼ & ∨ ⊃ ≡ ∀ ∃ ∴ (or use the palette to produce them)

4/24/06

Tutorial 25 Exercises h

4/24/06

Tutorial 25 Exercises g