Re: Minimal Logics in the 2020's: A Meteoric Rise

On 7/6/2024 6:28 PM, Richard Damon wrote:

On 7/6/24 6:41 PM, olcott wrote:

On 7/6/2024 5:22 PM, Richard Damon wrote:

On 7/6/24 6:08 PM, olcott wrote:

On 7/6/2024 4:02 PM, Richard Damon wrote:

The problem here is you logic doesn't actually allow for the necessaery references in it.
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Not at all. My logic is simply smart enough to reject
non-truth-bearers AKA expressions that are not valid
propositions. It does not stupidly falsely assume that
every expression is a valid proposition.\

>
Logic isn't "Smart", it follows its rules.
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Your rules are just inconsistent.
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When-so-ever true means provable and false means not provable
the meaning of these words proves that such a system cannot
get stuck in pathological expressions.

 And such a definition requires the system to be keep simple or it becomes inconsistant.
 

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LP := ~True(LP) has a cycle in the directed
graph of the elements of the expression related
to each other that Prolog and MTT detects.
>

 So, what value does True(LP) return?
 

True(L,x)  means x is true.
~True(L,x) means x is untrue which includes false and not a proposition.
True(L,~x) means x is false.
~True(L,~x) means x is unfalse which includes true and not a proposition.
True(L,LP) is false and True(L,~LP) is false which means LP
is not a proposition.

If it returns your error below, it fails to meet the requirements, as "nonsense" statement must return false.
 But then, not that false is true, so the predicate is in its problem.
 THe only answers are:
1) Not have a True Predicate.
2) Not allow that form of reference, even indirectly, which limits the power of the logic system.
 

?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
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>

 

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Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer