Newsgroups: comp.lang.prolog,sci.logic
Path: cantaloupe.srv.cs.cmu.edu!das-news2.harvard.edu!news2.near.net!howland.reston.ans.net!agate!news.mindlink.net!news.bc.net!newsserver.sfu.ca!fornax!jamie
From: jamie@cs.sfu.ca (Jamie Andrews)
Subject: Re: natural deduction program
Message-ID: <1995Feb23.044046.3974@cs.sfu.ca>
Organization: Faculty of Applied Science, Simon Fraser University
References: <3i84rj$t5f@news.compulink.com>
Date: Thu, 23 Feb 1995 04:40:46 GMT
Lines: 34
Xref: glinda.oz.cs.cmu.edu comp.lang.prolog:12317 sci.logic:9790

In article <3i84rj$t5f@news.compulink.com>, Gareth  <Gareth@idirect.com> wrote:
>Does anyone know where to find theorem proving software to do
>proofs like:
>
> a<b ^ b<c -> a<c 
> =================
>
>1 a<b ^ b<c         assumption
>---------------
>2 a<b -> b-a>0      1; defn. of '<'
>3 b<c -> c-b>0      1; defn. of '<'      
>4 b-a + c-b >0      2,3; x>0 ^ y>0 -> x+y>0
>5 c-a+b+(-b)>0      4; x+y=y+x
>6 c-a > 0           5; x+(-x)=0,x+0=x
>7 a<c               6; defn.of '<'
>8 a<b ^ b<c -> a<c  7; '->'I

     I think the best place to ask this would be sci.logic,
whence I have crossposted this... I remember it coming up there,
but I can't remember any names of packages.

>also, when translating english statement of proofs, how do you translate 'Let', as in
>"Let e be a left identity and f be a left identity for an operation.
>Then e = f"
>does "Let" suggest quantifiers or some level of assumption?

     In this case, it looks like you mean "forall e, forall f,
left-identity(e) & left-identity(f) => e=f".  But sometimes,
e.g. if we say "let B be the powerset of A", we're using B more
as an abbreviation for something else.

--Jamie.
  jamie@cs.sfu.ca
"Could you do the egg bacon spam and sausage without the spam then?"
