# Ł_{ℵ} (Łukasiewicz)

## Notes

This is refered to as Łukasiwicaz's continuum valued logic.
[Priest,
2001, 217]

## Based on

- Rules
- Uniform substitution (US)
- Modus Ponens for > (MP>)

- Axioms
- (A>B) > ((B>C) > (A>C))
- A > (B>A)
- (A>~B) > (B>~A)
- ((A>B)>B) > ((B>A)>A)
- ((A>B)>B) <-> (A+B)
- (A&B) <-> (~A + ~B)

[Priest,
2001, p218]
(Which points out that the last two axioms are often presented
as definitions instead.)

# Community requests

- If anyone knows of a tablaux proof procedure for this system,
I would be interested in hearing about it.
-JH

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This page was last modified on December 11th, 2006.