[FOM] Counting models

Andy Fugard a.fugard at ed.ac.uk
Mon Jul 2 08:27:43 EDT 2007

John McCarthy wrote:
> More powerful than counting the models of a theory is parameterizing
> them.  I've done it for propositional theories in
> http://www-formal.stanford.edu/jmc/parameterize.html.

Dear John,

Many thanks for the reply.

Do the counts fall out of this?  It's not obvious to me how?  I actually 
am interested in the counts themselves (for dirty empirical reasons).

Also to get, e.g., syllogisms in that framework, my understanding is 
that you have to propositionalise, and then that gives you Herbrand 
models.  (Which is interesting too.)

For instance

   all x. P(x) => Q(x)
   all x. Q(x) => R(x)
   exists x. P(x)

would be transformed into something like

   P => Q
   Q => R
   P1 => Q1
   Q1 => R1

Arm-waving slightly this seems to extend to any monadic predicate 
formula?  But I have never absorbed the proofs.



Andy Fugard, Postgraduate Research Student
Psychology (Room F15), The University of Edinburgh,
   7 George Square, Edinburgh EH8 9JZ, UK
Mobile: +44 (0)78 123 87190   http://www.possibly.me.uk

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