4th Family Member: Relevant Logic (Was: Advent of Logic 2024: Weekend 3)

Hi,
Now that Christmas is over, are you excited for the new year?
Here is the task for Weekend 4:
- Do the same as for Weekend 2 and Weekend 3
   for a relevant logic.
This would complete the picture, since we would have:
Logic           Weakening      Contraction
Minimal         Yes            Yes
Relevant        No             Yes
Affine          Yes            No
Linear          No             No
Bye
Mild Shock schrieb:

Hi,
 Create a proof search in Simple Types,
that finds Lambda Expressions as proof,
for a given formula in propositional logic.
 The logic is the same as in Weekend 2.
 Bye
 Mild Shock schrieb:

Hi,
>
Create a proof search in Combinatory Logic,
that finds a Combinator Expression as proof
for a given formula in propositional logic.
>
The propositional logic can do with
implication only, and it should be Linear Logic.
French logician Jean-Yves Girard is credited
>
with Linear Logic, and since we have implication
logic only, the Logic will be also affine, i.e.
it will have no contraction, which makes
>
it special towards certain paradoxes.
>
Bye
>
Mild Shock schrieb:

Hi,
>
Draw a Colored ASCII Christams tree with Prolog.
>
Bye

>