From: pat hayes (phayes@ai.uwf.edu)
Date: 10/29/02
> > [Jerry] > As the expert in branching futures, how would you feel about ....? > >Well, speaking as the expert in branching futures, the current >ontology is a bit incoherent. It is mostly concerned with time >_measurement_. From that point of view it would be meaningless to >talk of branching time, because even if you think there are multiple >versions of next week, they presumably all start Wednesday at the same >"date." > >The only place where the ontology connects to actual events is in >section 2.5, where the 'holds' predicate is introduced. But the >treatment there is sketchy. For instance, we have the following: > > during(e,T) & inside(t,T) --> at-time(e,t) > >Intuitively, this would be true only if 'e' is some kind of >proposition, such as "The cat is on the mat." If 'e' is "Sir Fred >bowing three times to Queen Sally," in what sense does that hold at >every instant of an interval over which it occurs? Well, one can >craft one's ontology any way one wants, but in branching time there is >a real problem. Suppose that in one branch, after the first bow Sir >Frank rushes in and knocks Sir Fred to the floor. In another, Frank >is a little late and Fred completes his three bows. Now pick a time >instant in the middle of the first bow. By the axiom above Fred is >bowing three times at that instant, even though in some futures he >never gets to bow 2. > >I think it would be cleaner to separate time measurement from events >and other eventualities. The axioms can all stay the same, but we >drop the idea that a time instant is a situation in the McCarthy-Hayes >sense. Instead, we would have a function > > (sit-at ti pw) > >which denotes the situation that obtains at time 'ti' in the possible >world 'pw'. (If you would rather avoid time instants altogether, you >can also map an interval to a situation sequence or history or >something; I will leave that to others.) Then you set up >relationships among various possible worlds in the usual ways. Then >you make 'holds' a predicate on situations (or histories, mutatis >mutandis). Branching time is the case where if pw1 is an alternative >to pw2, then they share a prefix and nothing thereafter. I agree, except for the last sentence. I think that the idea of branching time is close to incoherent if we really want time to be something like a continuum, or even dense. (When does it branch, for example, and when does it just go on rolling along?) It is better to distinguish possible-timelines and times in a timeline, as orthogonal distinctions. One can think of these as two modalities, respectively possibility and tense. The discrete sit-calc picture is then a branching 'structure' defined over a set of timelines with a common time metric, like little arrows going from one line across to another. The structure is branching, more or less by definition; but the timelines aren't and they needn't even have a common past. Then it makes sense to ask things like, how long would it have been since you last went to Australia if you hadn't gone to Sydney last year? Possibility really hasn't got anything intrinsically to do with time. We can make firm predictions about the future, and we can be uncertain about the past. Thinking about planning tends to get these muddled together since one assumes sufficient knowledge about the present and not about the future (which is why one is planning in the first place, presumably), but that's only one way of thinking and may not be the primary one. Pat -- --------------------------------------------------------------------- IHMC (850)434 8903 home 40 South Alcaniz St. (850)202 4416 office Pensacola (850)202 4440 fax FL 32501 (850)291 0667 cell phayes@ai.uwf.edu http:/ http://www.coginst.uwf.edu/~phayes s.pam@ai.uwf.edu for spam
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