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Re: [ontolog-forum] using SKOS for controlled values for controlled voca

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Christopher Menzel <cmenzel@xxxxxxxx>
Date: Mon, 11 Oct 2010 11:42:33 -0500
Message-id: <A49627EE-4966-40C9-B391-EFED74B1E602@xxxxxxxx>
On Oct 8, 2010, at 6:48 PM, John Bottoms wrote:
> Can we say:
>   FOL is a subset of HOL.    (01)

Not really, at least under most definitions of the notion of a logic. This is a 
bit better: Let L be a first-order language and let L' be the result of adding 
second-order (and even higher-order, if you please) quantifiers to L.  Then 
every logical truth of L, under a standard first-order semantics, will be a 
logical truth of L', under a standard second-order semantics.  More generally, 
for any set S of sentences of L and any particular sentence A of L, if A is a 
logical consequence of S under a standard first-order semantics for L, then A 
is a logical consequence of S under a standard second-order semantics for L'.    (02)

Chris Menzel    (03)

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