Re: Logical = relational?
Date: 5 May 2006 09:48:30 -0700
Message-ID: <1146847710.815088.155230_at_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
ab - conjunction
1' - identity/diagonal relation
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).
^a - converse of a (a relation with interchanged 1st and 2nd attribute)
a;b - composition