From: Richard Fikes (fikes@ksl.stanford.edu)
Date: 06/25/02
As input to your writing and as a reminder, I sent a message to the committee on June 18 which included the following: > The proposal is to allow answers to contain bindings of distinguished > variables to 'null', and let the server return any answer it finds that > is not the same as or less specific than the previous answers it has > returned. (which is an easy filter for the server to apply before > returning an answer) > > The primary problem we had with that proposal was how to formalize what > the answer set is for a query, because what answers any given server > will produce is dependent on the order in which it generates the > answers. Here is the formalization that I proposed to deal with that > problem. Define a "super answer set" to be the set of all the answers > to a query that are entailed by the KB unioned with the less-specific > versions of each of those answers (e.g., if [?x/a ?y/b] is an answer in > the super answer set, then [?x/null ?y/b], [?x/a ?y/null], and [?x/null > ?y/null] are also in that set). Then define the "minimal answer set" to > be the subset of the "super answer set" in which no answer subsumes any > other answer. Finally, simply require the answers produced by a server > to be a subset of the "super answer set". The formal semantics would > specify the "minimal answer set" and the "super answer set" is a > straightforward extension of the "minimal answer set". That excerpt is the proposed "solution" to the sequencing and redundancy problem and includes the proviso that the server tests for redundant and less specific answers. You said at the beginning of last week's telecon that you agreed with my June 18 message. Also, when I mentioned that formalization of the answer set in an earlier message in April, you seemed to agree with it in the following response from you on April 15: > >>That situation is > >>not impossible to formalize. For example, we could define a "super > >>answer set" that contains all the less-specific versions of each of the > >>answers (e.g., if [?x/a ?y/b] is an answer in the super answer set, then > >>[?x/null ?y/b], [?x/a ?y/null], and [?x/null ?y/null] are also in that > >>set). We could then say that any given server produces a subset of the > >>"super answer set" and could then define the "answer set" as the subset > >>of the "super answer set" in which no answer subsumes any other answer. > >>Not pretty, but doable. > > I think it is very pretty. It keeps the processing requirements > clearly separate from the semantic requirements, and makes explicit > the computational burden which one takes on if one insists on keeping > them aligned, viz. the need to generate, in the worst case, all the > answers before delivering any of them in response to a request. Richard
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