# Re: Minimal logic valid?

*From*: Jan Burse <janburse@xxxxxxxxxxx>*Date*: Wed, 25 Jun 2008 23:06:03 +0200

translogi schrieb:

modus ponens is the theorem (p -> ((p->q) ->q)

(CpCCpqq in Polish notation)

Summary of our new notation gobbling:

- Lemmon style: Natural deduction style, but

instead of a tree, lines and reference numbers.

- Polish Notation: Formulas instead with infix

notation, with prefix notation

We can possibly enlarge this list of variantions

ad infinitum. Here are some more:

- Fitch style (*): Like lemmon style, but we can

eliminate repeating the context on each line.

Instead that each line looks like:

...

G |- A

We simply write:

...

A

This works for a great deal of natural deduction

style rules, except for abstraction:

...

G |- A

-------------

G\B |- B -> A

So in case of having this rule in a proof, we simply

use a new notational concept, namely we change the

indent.

B

| ..

| A

B -> A

Right? (Stil little bit redundant for abstraction, but

other non-minimal logic rules might profit a little

bit more, than just the minimal logic rules)

- Reverse Polish Notation(**): Formulas instead with infix

notation, with suffix notation. So instead Cpq, we

write pqC for p->q.

What else? Peirce alpha-graphs?

Bye

(*) http://en.wikipedia.org/wiki/Fitch-style_calculus

(**) http://en.wikipedia.org/wiki/Reverse_Polish_Notation

.

**References**:**Minimal logic valid?***From:*Jan Burse

**Re: Minimal logic valid?***From:*MoeBlee

**Re: Minimal logic valid?***From:*Jan Burse

**Re: Minimal logic valid?***From:*MoeBlee

**Re: Minimal logic valid?***From:*translogi

**Re: Minimal logic valid?***From:*Jan Burse

**Re: Minimal logic valid?***From:*Jan Burse

**Re: Minimal logic valid?***From:*Alan Smaill

**Re: Minimal logic valid?***From:*Jan Burse

**Re: Minimal logic valid?***From:*Alan Smaill

**Re: Minimal logic valid?***From:*Jan Burse

**Re: Minimal logic valid?***From:*Alan Smaill

**Re: Minimal logic valid?***From:*Jan Burse

**Re: Minimal logic valid?***From:*Alan Smaill

**Re: Minimal logic valid?***From:*Jan Burse

**Re: Minimal logic valid?***From:*translogi

**Re: Minimal logic valid?***From:*Jan Burse

**Re: Minimal logic valid?***From:*translogi

**Re: Minimal logic valid?***From:*Jan Burse

**Re: Minimal logic valid?***From:*translogi

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