Predicate Logic: 15 Tutorials admin Sat, 01/11/2014 - 01:50
Logical System

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

Beryl is a philosopher.
All philosophers are wise.
Beryl is wise.

Sentential Logic: Try your own derivations admin Sat, 01/11/2014 - 01:50
Logical System

Roll your own derivations


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 ∼ & ∨ ⊃ ≡ ∀ ∃ ∴

Supplementary: Why are we doing all these derivations anyway? admin Sat, 01/11/2014 - 01:50


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.

Tutorial 10: Common Inference Patterns and Rewrite Rules admin Sat, 01/11/2014 - 01:50
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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.


Bergmann[2008] The Logic Book Section 5.5

Another Example of a Harder Sentential Proof: One of De Morgan's Laws admin Sat, 01/11/2014 - 01:50
Logical System

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