On event hirearchies and types

In a comment to my previous posting Harvey has reminded me that Israel won second place ("gold medal") in the Chess Olimpics, actually it has been number one through part of the games and then moved to number two which is also very respectable. I have not played chess since high school, but I have registered to play in an internal IBM championship in Backgammon;
A game I have not played a lot recently, so need to practice...

I am following with interest Marco's Rulecore Blogging about geo-spatial operators, I think this is in the right direction, and there is a lot of potential in spatial and even spatio-temporal patterns and I also view space as one of the main dimensions of context. However, today I would like to write about one of the other topics that Marco has been writing about -- event hirearchies, in this posting Marco suggests hirearchy level of events and rules, such as rules in level 1 consume only events of level 1 and produce event of level 2, and so forth. This reminds me a great scholar named Bertrand Russell, whose picture you can see below:
Russell has introduced a well-known paradox which in its popular form is called the "Barber Paradox" (Wikipedia claims that
which states that in a village there is a barber who shaves everybody who does not shave himself. The question is who shaves the barber? if the barber shaves himself that means that the barber is not shaved by the barber, however if the barber shaves the barber that means that the barber does not shave himself, meaning that the barber shaves himself if the barber does not shave himself and vice versa. Russell also provided solution for the paradox called "type theory" saying that we have hierarchy of terms and functions/predicates based on "types". Thus if a "person" is of type 1, Barber is a predicate of a person, which makes it term of type 2, being a term of type 2, it cannot participate in predicates on type 1, and thus the entire paradox does not happen. Type theory indeed resolves the paradox (if you wonder the "types" in programing languages are indeed derived from Russell's terms), however, the price is that the expressive power of the language is compromised, things which seem to us perfectly valid in natural language are not valid under the types theory.

Back to event processing -- let's look at the following example:

• Our location-based event processing system manages fleet of cabs and travel reservation.
• An order arrives for a travel in 30 minutes
  - this is an event of type 1, it is processed and matched against taxis locations and directions to assign the right cab and makes "cab assingment" which is an event of type 2 (since it was created by an event processing agent - "rule" in Marco's terminology that processed events of type 1).
  
• After a short while the perspective traveller changed his mind and called to cancel the order. This is again, event of type 1.
  
• However, now we have to find out if the travel has already been allocated and if yes deallocate the travel and free the allocated taxi. This operation has to take two events as input -- the travel cancellation (type 1) and the travel allocation (type 2)... Oops... our system works purely on strict hierarchy of event types --- can't do that!.
  

This demonstrates that using strict hieratchy we'll have, like Russell's type theory, to give up expressive power. So it seems that while hierarchy is a good idea, it may also serve as a restriction... One modification is indeed to order the event types and the agents, however enable agent of type 2 to accept as input events at type 1 and 2.

With this correction there are certain benefits for using the hierarchy levels, relate to optimization possiblities that Marco have not mentioned. We'll discuss them in one of the next postings.