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From: Mild Shock <janburse@fastmail.fm>
Newsgroups: sci.logic
Subject: Re: Still on negative translation for substructural logics
Date: Mon, 2 Dec 2024 09:49:07 +0100
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Could it be that your procedure doesn't
terminate always? Why is this not finished
after more than 1 minute?

?- solve_case(TT, pelletier, G), time(solve_t__sel(TT, G)).
Action (h for help) ? abort
% 844,501,974 inferences, 63.891 CPU in 68.236 seconds (94% CPU, 
13217933 Lips)
% Execution Aborted

The test case was:

solve_case(neg, pelletier, []=>((p<->(q<->r))<->(p<->q))).

Or just a problem of explosion?

Julio Di Egidio schrieb:
> On 01/12/2024 15:32, Mild Shock wrote:
> 
>  > So although it was very temping to download
>  > you software, and then replace these line:
>  > <https://gist.github.com/jp-diegidio/b6a7a071f9f81a469c493c4afcc5cb11>
>  > By these line:
>  > notation(gliv(X), (~(~X)))
>  > solve_t__sel(neg, C=>X) :-
>  >     solve(C=>gliv(X)).
> 
> Or just change the definition of `dnt`, or create another one.  The code 
> is functional and pretty flexible actually, `notation/5` is `multifile`.
> 
>  > I am afraid I have no time for that. You
>  > could do it by yourself. Or what
> 
> I have already done it, and I have already told you the results!  You 
> have no time for anything apparently, except for posting random shit and 
> fucking with thread titles: I have messages all over the place, and it's 
> just me, you, and Ross once a month...
> 
> ---
> 
> Here is an interesting new case, which I had thought should be 
> *unsolvable*:
> 
> ```
> ?- solve_w([]=>dnt((~(~p)->p)<->p\/(~p))), !.  % DNE<->LEM
> ```
> 
> Unsolvable not just because my logic is *affine*, but because the actual 
> statement, provable intuitionistically, is intrinsically higher-order:
> 
> ```
> Theorem DNE_is_LEM : (forall p, ~ ~ p -> p) <-> (forall p, p \/ ~ p).
> ```
> 
> while the statement I am proving above is this one, and it is not 
> intuitionistically provable (AFAICT):
> 
> ```
> Theorem DNE_is_LEM_not_quite : forall p, (~ ~ p -> p) <-> (p \/ ~ p)
> ```
> 
> Yet with my `dnt`, my solver proves even that one (but I still have to 
> inspect the proof tree, what I actually get).  Indeed, I am rather 
> worried that it just solves everything I throw at it, though not the 
> falsities... which is why I am also developing a meta-theory for it, in 
> Coq:
> 
> <https://gist.github.com/jp-diegidio/b6a7a071f9f81a469c493c4afcc5cb11#file-gentzen-v> 
> 
> 
> -Julio