From: pat hayes (phayes@ai.uwf.edu)
Date: 10/16/00
>Ah, one where I can clarify: > >Dan Connolly writes: > > In what way is > > The class C is the disjoint union of the classes > > in the list L. > > not an assertion? > >[Full context of the quotation below.] > >(*) The class C is the disjoint union of the classes > in the list L. >is an assertion. > >However, the clause > the disjoint union of the classes in the list L. >is not an assertion and may be meaningless. > >I believe that Pat (Hayes) means to be asking what C is asserted (by >(*)) to be in this case. Yes. >I believe that Dan's answer would be that the assertion (*) is false. That isnt an answer, however. (What *is* the disjoint union of the classes in L, in that case? We've established that it isn't C, but what is it?) >An alternative answer might be that the assertion (*) is true, but >that "disjoint union" of a non-disjoint class set is ill-defined, >e.g., that (*) is asserting that C is some special "error object". >This is a more operational way to interpret the assertion (*). That is an answer, butI don't think its particularly "operational". This is the standard trick for talking about partially-defined things in a logic which requires everything to be defined, eg KIF uses this (the error object is called 'bottom', referring to its place in a semi-lattice, no Shakesperian pun intended.) But let me urge that rather than go this route, which has pitfalls of its own (do all the classes have to contain bottom? Does bottom count as a value when working out cardinalities?) it would be much better to just have the usual mathematical definition of disjoint-union which always has a value, so no problem. >Dan and Pat (and everyone else), did I put the right words into your >mouths? Yes, from me. Pat --------------------------------------------------------------------- IHMC (850)434 8903 home 40 South Alcaniz St. (850)202 4416 office Pensacola, FL 32501 (850)202 4440 fax phayes@ai.uwf.edu http://www.coginst.uwf.edu/~phayes
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