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Q2
May 30, 2011 12:00PM
(i) ????
(ii) Used Def 1.36
(iii) Used Theorem 1.37
avatar Re: Q2
May 30, 2011 01:54PM
i. Something that can be proven without premises.
In shorthand: "... one zilch here ..." |- "Some Snazzy Greek Letter Here"

But that's a "COS261 answer", so I need to look up the new version.

ii. OK I go for the earlier style answer first, and then I'll look up the book.
A tautology is something whose truth table evaluates to T for every possible valuation of the atomic propositions of its premises.

T
T
T
...
...

Then we have T whenever all T: That's "entails" (falls short of a tautology).

So now I look and see how wildly wrong I am...
Tautology ... almost exactly right. Neat shorthand answer would be " ... zilch ..." "|=" Phi. So a tautology is to semantic entailment as a theorem is to proof-by-rules.

And I'm not too terribly wrong with the "entails" story either.

Phi. Rho. Chi. Phi2. More Premises Here. |= Poseidon.

The symbol |= is expressed in English as "semantically entails", meaning those premises semantically entail some conclusion. (Taut has no prem).

But what does "semantically entails" mean?? ... Whenever ... (see up there somewhere, above).

iii. These are logically equivalent things. They express exactly the same relationship in different ways.

So one could expand on that and say that Soundness and Completeness are equivalent.

Point iii could do with a bit of a critique....
Re: Q2
May 30, 2011 02:52PM
Keep in mind tht the quest is only worth 2 marks and I dnt think we supposed to giv a lengthy proof...
avatar Re: Q2
May 30, 2011 02:58PM
Outside the exam room I find saying it several different ways sometimes helps it stick a bit better. Yes, in an exam one would want to be a lot more terse. Sadly, sometimes I get distracted by interesting questions during exams ...
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