From owner-cse663-fa08-list@LISTSERV.BUFFALO.EDU Tue Sep 23 08:56:05 2008
Date: Tue, 23 Sep 2008 08:55:54 -0400
From: "William J. Rapaport"
Subject: 663: HW #1 - hints
To: CSE663-FA08-LIST@LISTSERV.BUFFALO.EDU
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Subject: HW #1 - hints
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Several of you are having trouble with HW #1. Parts of it, at least,
are easier than you may think.
For p.28, #1, for example, you need to specify a domain D, and then find
an interpretation of predicate P and constant "a" that will make the
sentences have the required truth values.
For a really strong hint, try taking D to be something like the set of
people, P to be a relation like "being the father of", and "a" to be
some person (give the person a name).
From owner-cse663-fa08-list@LISTSERV.BUFFALO.EDU Tue Sep 23 09:01:20 2008
Date: Tue, 23 Sep 2008 09:01:08 -0400
From: "William J. Rapaport"
Subject: 663: HW #1 - more hints
To: CSE663-FA08-LIST@LISTSERV.BUFFALO.EDU
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Subject: HW #1 - more hints
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A student writes:
>
> I'm having a lot of difficulty with #1 of the homework. In particular,
> I'm having a problem coming up with an interpretation for #1c: AxAy.P(a,
> y) > P(x, b).
>
> Are we to assume that a and b are constants?
Yes. See BL, p. 17.
> I've manage to come up with some interpretations for 1a and 1b that
> work, but I can't make the interpretations fit for 1c without making 1c
> into nonsense.
You will need different interpretations. So, you'll need one
interpretation that makes (a) true and the others false, another
interpretation that makes (b) true and the others false, and yet another
interpretation that makes (c) true and the others false.
> Is it possible to get an extension on the homework?
Ask me in class on Wednesday morning :-) In the meantime, keep trying!
From owner-cse663-fa08-list@LISTSERV.BUFFALO.EDU Tue Sep 23 13:12:33 2008
Date: Tue, 23 Sep 2008 13:12:22 -0400
From: "William J. Rapaport"
Subject: 663: HW #1 - yet another hint
To: CSE663-FA08-LIST@LISTSERV.BUFFALO.EDU
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Subject: HW #1 - yet another hint
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When trying to find interpretations that make a material-conditional
statement false, keep in mind that such a statement is true if it has a
false antecedent. So, e.g.,
Ax[(x is the mother of y) ^ (y is the mother of x) > x=y]
will be TRUE if x is the mother of y, because: if x is the mother of y,
then y is not the mother of x; therefore, the antecedent is a
conjunction of a true and a false sentence. So, the antecedent is false.
Consequently, the conditional is true!
Be careful that your interpretations don't fall prey to this potential
error.
On the other hand, you may be able to use this to your advantage in
finding appropriate interpretations :-)