Exploiting Domain structure to Achieve Efficient Temporal Reasoning

We take temporal reasoning to be the problem of ma in ta i n i ng a set of constraints between t i m e po in ts a n d / o r intervals, and responding to queries about the tempora l separat i on between those ind iv idua ls . Forma l invest i gat ions of th is constra int -sat is fact ion p rob lem have demonst ra ted tradeoffs between the expressive power of the constra int language and the t i m e required to answer queries. A s imple constra int language admi ts an a lgo r i t hm cubic in the number o f ind iv idua ls ; a l lowing unrest r ic ted d is junct ive constraints makes the a l g o r i t h m exponent ia l . The prob lem is tha t app l icat ions of t empora l reasoning, e.g. p lan proj ec t i on , need bo th d is junct ive constraints and an a l go r i t hm much faster than 0 ( n 3 ) . I t is s igni f icant , however, t ha t the nature of the constra ints added by and the queries posed by an app l ica t ion tend to be s t ruc tured and pred ic table. Our so lu t ion to the p rob lem is to exp lo i t the s t ruc ture o f the app l ica t ion doma in to prov ide fast responses to typ ica l queries. We consider the p rob lem of p lan project ion under uncer ta in ty and bu i ld a tempora l representat ion—hierarchical in terval const ra ints ( H I C ) — t h a t al lows appropr ia te disj unc t i ve constra ints. We then implement the H I C representat ion in a temporal reasoning modu le , and test i t using a p lan-pro jec t ion app l i ca t ion . A p p l y i n g the H I C modu le to a s imple t empora l p ro jec t ion p rob lem shows orders-of -magni tude improvement over runn ing the same pro jec tor using current imp lementa t ions o f domainindependent tempora l cons t ra in t propagators.