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P1788, and Baker Among the comments on the text under vote for Motion 31 was the following: On 27 Jan 2012, at 13:30, Vincent Lefevre wrote: > Comparisons mainly come from Motion 13.04, but a weakness of this > motion was that it gave an implementation -- namely in terms of endpoints, for the case of nonempty intervals -- > not the meaning as set > (or topological space) functions. I agree with this criticism. The present specification runs the risk that the empty set's behaviour (possibly that of unbounded intervals too) is ad-hoc, and might even be contradictory. So I have defined each relation by a predicate purely about set membership. I've also made several notational changes. The resulting revision of V04.4§5.6.9, and its Table 5, is attached. Though the text is short there seems quite a lot to say about it, as follows. - These definitions should make it easy to express the relations in terms of Jürgen's primitive overlap relation (§5.7.2) as they use the same notation. - There was criticism of the name "precedesEqual" since it makes this relation sound reflexive (precedesEqual(X,X) holds), which it isn't. So, in discussion with Vincent, I've renamed "precedesEqual" and "precedes" to "precedes" and "strictlyPrecedes"; and for consistency done the same to "lessEqual" and "less". If you like the old names better, or can propose a better scheme, please say. - I also renamed "containedInInterior" to "isInterior" simply because it was so long. Its set-theory definition is the straight topological one, on the grounds that it is standard, and simple to express. - Also, its symbol used to be just \subset, which was also rightly criticised because its standard meaning is just "a proper subset of". So I've invented a new symbol, which IMO expresses the "interior" idea quite well. - I also don't like the symbol for "precedes" (formerly "precedesEqual") because the line beneath suggests it's reflexive; but have not found an alternative that I like. - Should "areDisjoint" be renamed? The plural looks strange alongside "isEqual". I claim these set theory definitions are the simplest that agree with Ulrich's specification for compact nonempty intervals. We may find some of the results unexpected for empty or unbounded intervals. But we should accept them because anything else is logically more complicated. I propose this text should replace the present §5.6.9. Baker, I apologise for bringing this forward so late. Does this mean the current Motion 31 must be withdrawn? Or suspended pending a vote on this as an amendment? What is the correct procedure? Regards John Pryce
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