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Re: [ontac-forum] Before we start...

To: ONTAC-WG General Discussion <ontac-forum@xxxxxxxxxxxxxx>
From: "Smith, Barry" <phismith@xxxxxxxxxxx>
Date: Sat, 21 Jan 2006 18:53:12 +0100
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>John writes:
>In previous discussions, I stated one definition of type, and
>Barry stated another.  The the pros and cons of either one are
>moot points, since the semantics of "type" will be determined
>by whatever version of logic is adopted.  If CL is the logic,
>then types would be represented by monadic relations in CL,
>which would be represented as restrictions on the quantifiers
>in typed dialects of CL.  An instance of a type would be anything
>in a given model for which the corresponding relation is true.    (01)

I note that there is a second way in which types can be represented 
in CL, which I am confident John will agree is possible:    (02)

we introduce two sorts of individual variables,    (03)

x, y, z ... for instances (particulars)    (04)

u, v, w ... for types    (05)

together with a two-place predicate instance_of to assert things like    (06)

Fido instance_of dog.    (07)

In this way we can quantify, harmlessly, over types, and yield 
(albeit trivially) some of the benefits of second-order logic.
BS     (08)

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