Re: higher Order Logic, and Oyster Clam

OK, I was afraid of this, getting into deep waters here :-)

> On Jun 26, 2019, at 12:40 AM, Paola Di Maio <paola.dimaio@gmail.com> wrote:
> 
> In relation to RDF and FOL
> 
> Just thinking loud (not asking any question)
> 
> I know that there is an underlying argument that all logic is essentially FOL

I wouldn't make that strong a claim. There certainly are other logics. 

> (never mind exceptions and other POVs
> 
> Was going through some papers and some relevant points came up
> 
>   Automation of Higher-Order Logic 
> Authors: Christoph Benzm¨uller and Dale Miller Readers: Peter Andrews, Jasmin Blanchette, William Farmer, Herman Geuvers, and Bruno Woltzenlogel Paleo Venue: The Handbook of the History of Logic, eds. D. Gabbay & J. Woods Volume 9: Logic and Computation, editor J¨org Siekmann   
> http://www.lix.polytechnique.fr/~dale/papers/automationHOL.pdf <http://www.lix.polytechnique.fr/~dale/papers/automationHOL.pdf> 

I was using the term ‘higher-order’ in the way described here (section 2.2, page 7) as the way that ‘philosophers of mathematics’ use it, in which higher-order quantifiers range over the universe of /all/ functions. There are those who would describe some logics that I call first-order as being higher-order (or, HO syntax with nonstandard models, or Henkin HO logics, or F-logic, or several other terms.) ISO Common Logic for example is such a logic. It is HO in its syntax, so it “looks like” higher-order, but has a strictly first-order semantics, and so can be handled by FO reasoning engines. And it is FO by the criteria of the Lindstrom theorem. 

Pat

> 
>   Bundy, A., van Harmelen, F., Horn, C., Smaill, A., 1990. The Oyster-Clam system, in: Stickel, M.E. (Ed.), 10th International Conference on Automated Deduction, 
> 
> Computational Logic  Page 145
> https://books.google.com.tw/books?id=H9-pCAAAQBAJ&lpg=PA145&ots=AidwU3D11M&dq=oyster%20logic&pg=PA145#v=onepage&q=oyster%20logic&f=false <https://books.google.com.tw/books?id=H9-pCAAAQBAJ&lpg=PA145&ots=AidwU3D11M&dq=oyster%20logic&pg=PA145#v=onepage&q=oyster logic&f=false>
>