Re: Logical = relational?

From: Mikito Harakiri <mikharakiri_nospaum_at_yahoo.com>
Date: 5 May 2006 09:48:30 -0700
Message-ID: <1146847710.815088.155230@i40g2000cwc.googlegroups.com>

J M Davitt wrote:
> Mikito Harakiri wrote:
> > In modern notation Tarski algebra includes five logical
> > constants/operations:
> > 0, 1, -a, a+b, ab
> > and five relational counterparts:
> > 0', 1', ^a, a^+b, a;b
>
> Could you name these "five logical
> constants/expressions" and the "five relational counterparts?"

This snippet is from Vaughan Pratt paper "Origins of the calculus of Binary Relations".

0 - the least element in BA
1 - the greatest element in BA
-a - complement of a
a+b - disjunction (or since it is algebraic perspective is it actually sum modulo 2?)
ab - conjunction

1' - identity/diagonal relation
^a - converse of a (a relation with interchanged 1st and 2nd attribute) a;b - composition

Those are standard 8 operations that can be found in any article about binary relational algebra (BRA). I refer you to Pratt paper for the remaining 2 operations/constants (I don't quite understand them myself). Received on Fri May 05 2006 - 11:48:30 CDT