FOM: Re: SOL confusion
V.Sazonov at doc.mmu.ac.uk
Thu Sep 7 14:14:20 EDT 2000
As to terminological confusion related with SOL, there is another
usage of the term `logic', say, in finite model theory or descriptive
complexity theory which seems to me not very natural. Say,
FOL + LFP (LFP = `Least Fixed Point operator') is called `logic'
where it shoud be used the term `language'. It is considered
only definability in such "logics", without involvement of any
inference mechanism. It seems that more consistent to use `logic'
only if it is a system of reasoning. Therefore SOL is better to
read as `Second Order Language' (and analogously in other cases)
when only semantics of SOL is considerd. Then `Second Order Logic'
should mean one concrete formal system or a family of formalisms
based on the corresponding language. Unfortunately, the
abbreviation `SOL' remains ambiguous.
On the other hand, we know that ambiguity of a (natural) language
makes it simpler. We usually understand from the context what
is assumed. At least, when necessary, we should be more precise,
as the discussion on SOL proves.
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