derivations

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 ∼ & ∨ ⊃ ≡ ∀ ∃ ∴

And the right syntax (the premises separated by commas and then a 'therefore' followed by the conclusion).

3/16/06

So that we can show certain arguments to be valid.

The focus of the course lies with the validity and invalidity of arguments. Now, invalidity can be established by counter-example (by producing an interpretation under which all the premises are true and the conclusion false, at the same time). But validity is a different matter. And the usual approach is to have rules of inference and to do derivations.

Replacement or Rewrite Rules

6/21/07

Rewrite Rules

This video uses '&' as the logical symbol for 'and'.

2013

Skills to be acquired

Becoming familiar with common inference patterns and being able to use them via three new rules of inference and via rewrite rules. This helps with assessing ordinary everyday reasoning such as that found in the law, in newspapers, in advertisements, etc.

Reading

Bergmann[2008] The Logic Book Section 5.5

Example of a Harder Propositional Proof: One of De Morgan's Laws

10/23/06

Example

Example of a Harder Propositional Proof

2/27/06

Example

2013

Skills to be acquired:

Learning the Rules Or Elimination and the Introduction of the Biconditional.

Reading

Bergmann[2008] The Logic Book Section 5.1 and 5.4

The Tutorial:

Or Elimination, in the guise of Dilemma, also is a form of inference dating from antiquity.

Reductio ad Absurdum

2/24/06

Absurd Introduction and Simple Reductio

1/10/2020

Skills to be acquired:

Learning reductio proof, both as plain Negation Introduction and via (double) Negation Elimination (to prove some formulas that do not have negation as their main connective).

Reading

Bergmann[2004] The Logic Book Section 5.1 and 5.4

The Tutorial:

Reductio ad Absurdum is the second of the classical forms of inference.

9/12/06

Conditional Proof

This video shows the techniques for Conditional Proof using the downloadable application Deriver. But the techniques are exactly the same for the Proof applet running in a web page. So, the video may look slightly different to what you are looking at, but the underlying principles and approach are the same.