[FOM] quantifiers as sentential operators

[Alasdair Urquhart]

> What are the advantages and disadvantages of forcing quantifiers to be
> treated as "sentential operators"? (say, by indexing them with their
> variables)
>
> Does that even make sense, from a linguistic, an algebraic or a
> computational perspective?
>
> Reactions and references are welcome.

It definitely makes sense, because that is exactly the approach
taken in the theory of cylindric algebras.  It can be
considered as a form of multimodal logic, where you have
countably many S5 modal operators, one for each variable.

Alasdair Urquhart