Path: ...!weretis.net!feeder8.news.weretis.net!reader5.news.weretis.net!news.solani.org!.POSTED!not-for-mail
From: Mild Shock <janburse@fastmail.fm>
Newsgroups: sci.logic
Subject: Challenge 2025: Strict Forest for Relevant Logic
Date: Wed, 8 Jan 2025 12:19:35 +0100
Message-ID: <vlln06$2078b$1@solani.org>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Wed, 8 Jan 2025 11:19:34 -0000 (UTC)
Injection-Info: solani.org;
	logging-data="2104587"; mail-complaints-to="abuse@news.solani.org"
User-Agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64; rv:91.0) Gecko/20100101
 Firefox/91.0 SeaMonkey/2.53.19
Cancel-Lock: sha1:KP3ZBXH9tdyoUiifaCjFPhTko+4=
X-Mozilla-News-Host: news://news.solani.org:119
X-User-ID: eJwNy8EBwCAIA8CVREiAcYrI/iPY+x+UwuNG0DCYFWqSxzWl/Qu006yw4ctvr7hnwrZMTigpVoJsqcL/M/0+IaUUOA==
Bytes: 1838
Lines: 30

Hi,

Ok, I am an ornithologe that is mainly
interested in strict forests , where there
are no mocking birds, since everything

is simple typed. Now among the strict forests,
are certain forests that follow a multi-valued
logic. Basically each bird group is a law of a

multi-valued logic. Like for example these bird
groups, the type parameters are given in curly brakets:

I{X} : (X -> X)
B{X,Y,Z} : ((Y -> Z) -> ((X -> Y) -> (X -> Z)))
C{X,Y,Z} : ((X -> (Y -> Z)) -> (Y -> (X -> Z))))
S{X,Y,Z} : ((X -> (Y -> Z)) -> ((X -> Y) -> (X -> Z)))
K{X,Y} : (X -> (Y -> X))
W{X,Y} : ((X -> (X -> Y)) -> (X -> Y))

Here is an example multi-valued logic, Łukasiewicz
three valued logic, that satisfies B, C and K, but not W:

(0->0)=2 (0->1)=2 (0->2)=2
(1->0)=1 (1->1)=2 (1->2)=2
(2->0)=0 (2->1)=1 (2->2)=2

Is there a multi-valued ogic, that satisfies S, B, C
and I, but not K?

Bye