FOM: Re: SOL confusion

[V. Sazonov]

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. 


Vladimir Sazonov