Subject: HW#3
From: "William J. Rapaport" <rapaport@buffalo.edu>
Date: Wed, 23 Sep 2009 20:39:07 -0400 (EDT)

A student writes:
"I am having a problem in choosing the predicates. In the example for
problem #4 of HW #3, you have given 'Some dogs are pets.'

Here it is given Dog(x)= x is a dog.
                 Pet(x)= x is a pet.
then it is Ex[Dog(x) ^ Pet(x).

But is there any difference if I let the domain be dogs, and then just
write ExPet(x)?"

Reply:
Good point: You can do it either way. You always start by specifying
the domain, and then the syntax & semantics of the predicates you want
to use.

My example assumed that the domain was: everything in the universe. In
that case, to say that some dogs are pets, I have to have an explicit
"is a dog" predicate: Dog(x).

The way you propose to do it, your domain the just the set of dogs, so
you don't have to specify an "is a dog" predicate, because, almost by
definition, everything is a dog. All you have to say is that some of
them are pets: ExPet(x).