gentzen

2013

Some predicate logic proofs or derivations using Gentzen calculus. Try to prove them. Click on a line to select it. Select one or more lines, apply the appropriate rule off the Rules menu. (Click 'Derive It' off the Wizard Menu, if you want help).

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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

4/24/06

Tutorial 25 Exercises e

4/24/06

Tutorial 25 Exercises d

4/24/06

12/26/13

You now have the tools to appraise arguments to the level of detail offered by predicate logic.

Let us run through how these might be used with a long and difficult example.

Consider the argument

9/13/20

Skill to be acquired:

To understand the concepts of scope, free, bound, and free for.

Why this is useful:

The new predicate rules of inference using quantifiers have restrictions on them which are expressed in terms of these concepts.

12/24/13

The Tutorial

The semantics of relations proceeds in much the way one would expect-- the new item that has to be taken account of is the order of the terms (because, for example, Tab is not at all the same thing as Tba -- Arthur being taller than Beryl is not the same as Beryl being taller than Arthur).

Let us start with an Interpretation

Interpretation 1

Universe= {a,b}
F={a}