Re: Minimal logic valid?



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
.