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Date: Tue, 29 Sep 92 20:47:13 -0700 From: John McCarthy <jmc@sail.stanford.edu> Message-id: <9209300347.AA23509@SAIL.Stanford.EDU> To: sowa@watson.ibm.com Cc: SRKB@ISI.EDU, INTERLINGUA@ISI.EDU, CG@cs.umn.edu, buvac@cs.stanford.edu, costello@cs.stanford.edu, guha@mcc.com In-reply-to: sowa@watson.ibm.com's message of Tue, 29 Sep 92 22:03:11 EDT <199209300208.AA01752@venera.isi.edu> Subject: More about contexts Reply-To: jmc@cs.stanford.edu

The contexts that Guha and Sasa Buvac and I have studied are a lot more ambitious than any of the three possibilities you list, and I think this greater ambition is appropriate to Intelingua/KIF. Your three notions are: 1. A packaging mechanism for enclosing a collection of formulas and allowing them to be named and referenced as a single unit. 2. The contents of that package, which could be called anything from "quoted formula" to "microtheory". 3. The permissible operations on the formulas in the package. These operations could be defined by a set of axioms in a larger package that encloses the one under discussion. You choose the packaging mechanism alternative and give the following examples. 1. "The conjunction of the formulas in this box is false." 2. "The formulas in this box describe a possible state of affairs." 3. "Mary believes the propositions stated by the formulas in this box." 4. "The formulas in this box interact according to the axioms contained in the box named S5." 5. "The formulas in this box were true during the time interval [t1,t2]." 6. "Any formula placed in this box must be in Horn-clause form." None of the six examples relate formulas in the box to formulas outside the box. Our work is entirely based on {\it lifting formulas} that relate a formula in an inner context to formulas outside the box. Examples: A certain context c1 may refer to a fixed time interval. In that context a formula at(McCarthy, residence(McCarthy)) may be true. To lift this formula out of the context into a more general context c2 in which the referent of "McCarthy" is defined but a specific evening is not, we use a lifting relation ist(c1,p) iff ist(c2, holds(1992 Sept 29 8pm-9pm,p)). To lift the formula to a more general context c3 in which "McCarthy" hasn't a definite referent, it is necessary to use another lifing relation. I think even the simplest applications to databases require formulas that change on lifting. To take an example from our recent proposal, the Airforce, the Navy, and General Electric Company may all have databases of airplane engines and their prices, but they may differ in assumptions about spare parts. Using the databases together requires a more general context to which the formulas from the specialized databases can be lifted but translated appropriately. I'm sure that communication among programs will also require lifting relations.