On Mon, 2010-10-11 at 12:41 -0700, Rich Cooper wrote:
> That may be true from a purely logical sense, but only for that sense. (01)
Well, that's just fine, as that's the only sense I had in mind. (02)
> HOLs have a long and valued history, from Fortran I through SQL and
> further, and they do much more than mere logic. (03)
Mere logic? You do realize what the "L" in "HOL" stands for, right? (04)
> They represent aspects of reality that model what we believe to be
> valid, real world mechanisms. (05)
You are using "Higher-order logic" in what appears to be your own
idiomatic sense. The expression has a very clear meaning among
mathematical logicians and theoretical computer scientists. And it is
in no wise part of the definition of higher-order logic that it
"represents aspects of reality that model what we believe to be valid,
real world mechnisms." Logics of many different kinds have been used to
represent aspects of reality. Higher-order systems have no monopoly
on this. (06)
> For example, global warmers are using simulation of weather processes
> that would be completely meaningless to observers in a pure FOL
> expression. (07)
This remark is so confused on so many levels that it is hard to know
where to begin. (08)
> A well developed HOL is far more expressive than logic, more readable,
> communicable, and therefore more able to be tested for validity in
> reality as compared to simple expression of theories that may or may
> not be validated by experience. (09)
Again, it is apparent that you are simply using "higher-order logic"
in a sense all your own. (010)
> Pure FOL, in its original, very limited form, is fit for mathematical
> expositions of very small issues. And yes, theoretically it can do
> anything that the other languages above can do. (011)
Well, I'm not sure what you mean by what a logic can "do", but there are
clear senses in which FOL cannot "do" what higher order logics can "do". (012)
> But that is not the reason to stick to FOL when more expressive and
> communicable languages abound. (013)
Higher-order languages are indeed more expressive. As a consequence,
they are not even partially decidable. (014)
> So, strictly speaking, the "subset" isn't well chosen as a description
> of the difference, as you mentioned and explored in your email. But
> very, very little work is done in pure FOL anymore. (015)
I have no idea what you mean by "pure" FOL, but the fact is that much of
what is going on in Semantic Web research is done in FOL or a fragment
thereof -- notably, everything for which OWL is used. This doesn't
count as "work" for you? (016)
> A better description would be "FOL is less expressive than many HOLs". (017)
It's less expressive than all of them under standard semantics. (018)
> HTH, (019)
HTH? Not likely. (020)
Chris Menzel (021)
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