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*To*: lojban-list@snark.thyrsus.com*Subject*: theory of intervals*From*: cbmvax!uunet!glia.biostr.washington.edu.biostr.washington.edu!jsp (Jeff Prothero)*Posted-Date*: Wed, 9 Jan 91 14:20:40 PST

I've long wanted Loglan to apply the described "theory of intervals" to tense construction etc. One pet peeve I like to bring up annually: Time, in contemporary physics, and increasingly in practical experience as well, is a partial order, not a complete order. That is, given two spacetime events A and B, the possible orderings are: A before B A coincident with B A after B A incomparable with B <--- frequently ignored case. (If the fourth case doesn't make sense to you, you need to consult the standard light-cone diagram in any standard "ABCs of Relativity" popular-science book/article...) Any linguistic facility naming interval relationships by enumerating possible endpoint orderings should (IMHO) be based on the above partial order rather than the traditional Newtonian full order. Thus, the standard (?) interval enumeration for two intervals A=[a,a'] B=[b,b'] 01) a < b a' < b "A before B" 02) a < b a' = b "A until B starts" 03) a < b a' in b "A until B" 04) a < b a' = b' "A until B ends" 05) a < b a' > b' "B during A" 06) a = b a' in B "A during B" 07) a = b a' = b' "A while B" 08) a = b a' > b' "B during A" 09) a in B a' = b' "A during B" 10) a in B a' > b' "A starting in B" 11) a = b' a' > b' "B until A starts" 12) a > b' a' > b' "A after B" should really be augmented with the following intervals ("?" ::= "imcomparable to"), each of the above cases with a "=" giving rise to a case with a "?": 13) a < b a' ? b 14) a < b a' ? b' 15) a ? b a' in B 16) a ? b a' = b' 17) a = b a' ? b' 18) a ? b a' ? b' 19) a ? b a' > b' 20) a in B a' ? b' 21) a ? b' a' > b' Jeff Prothero jsp@milton.u.washington.edu Better a bicycle without wheels than a loglan without formal semantics!

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