The object of this section is to give narratives illustrating the treatment of concurrent events in two cases. The first is when two sub-narratives do not interact, and the second is when they do. The first sub-narrative is ordinary block stacking (as discussed in many situation calculus papers), and we suppose the stacking to be done by a person called Daddy in New York. In the second sub-narrative, the actor is named Junior, and he wants to fly from Glasgow to Moscow via London. The story is taken from an earlier unpublished but widely circulated manuscript [McCarthy, 1992] discussing how circumscription could be used to treat an unexpected obstacle to a plan. In this case, Junior may or may not lose his ticket in London. The change is made by adding a single sentence to the facts. Without that sentence, one can conclude that flying to London and then to Moscow will get Junior to Moscow. With it he must buy another ticket in London, i.e. we can no longer conclude that the original sequence of actions will work, but we can conclude that the revised sequence that includes buying a ticket in London will work.
Because we want to treat interacting events, we make life more complicated for Junior. If he loses his ticket, he must wire Daddy in New York for money. Daddy, who normally indulges Junior, has to interrupt his block stacking and sell a block in order to get the money to send Junior.
In this narrative Junior doesn't lose his ticket and gets to Moscow without asking for help. Daddy stacks blocks in New York. There is no interaction, and nothing is said about the time relations between the two sub-narratives.
When Junior is in London, inertia gets us that the flights still exist, and Junior still has Ticket2. As for Ticket1, we would infer that he still has it unless we brought in the fact that a ticket is used up when one takes the flight the ticket is for. That is certainly a part of the knowledge of anyone who travels using tickets. Thus someone who had travelled by bus would infer it about airplane travel. Indeed it could be inferred from more general principles about commerce, e.g. that a seller doesn't want to allow the buyer to get an arbitrary number of what he has a paid for one of. However, anyone who travels has the more specific information and doesn't need to infer it from general principles about commerce. Indeed he may never have formulated any general principles about commerce.
Now we begin Daddy's life as a block stacker. We have stated no relation between the situations S0 and S0' and know nothing of their temporal relations. If we asserted
then we could conclude that Junior still had the tickets in S0'. Also asserting S0' = S0 would do no harm to the conclusions drawn about either subnarrative. We have asserted that Daddy has the three blocks mentioned, and we would like to be able to draw the nonmonotonic conclusion that these are all the blocks he has.
We can imagine that blocks being clear is a precondition for moving them. The preceding subnarrative does not violate this precondition, but in a narrative we don't ordinarily have to show that preconditions are satisfied. We should be able to conclude via inertia that Daddy has the three blocks in the final situation.
Now Junior loses the ticket and sends a telegram to Daddy asking for money. Daddy, who normally indulges Junior, sells a block and sends Junior the money, who buys a London-Moscow ticket and goes on to Moscow. I chose a telegram rather than a telephone call, because I would not want to tell about a telephone call as a sequence of statements by Junior and Daddy but rather to regard its result as a joint action, e.g. an agreement that Junior and Daddy would do certain actions.
Note also we haven't treated what Daddy now knows as the result of the telegram. It seems that treating knowledge and treating agreement are similar in their requirement for treating intentional entities. The intentional state that Junior has requested that Daddy send him the money is not merely that Daddy knows that Junior wants Daddy to send him the money. Also the agreement is likely to have something like a bit of narrative as an argument, e.g. a set of actions that Junior and Daddy will do with only partial time relations between the actions.
Up to here, narrative 2 is the same as narrative 1. Also insert here the sentences between equations (16) and (31).
We want to regard losing the ticket as something that happens to Junior rather than as something he does. That's why we don't write . The bad consequences of doing the latter would arise when we get around to writing laws that quantify over voluntary actions.
We will use some of the same names now for situations that are different than in narrative 1.
Interpolating unconnected situations and events into a narrative should not harm the conclusions. For example, we could put situations S0.5 and S0.7 between S0 and S1, i.e. time(S0) < time(S0.5) < time (S0.7) < time(S1), and suppose that Junior reads a book on the airplane during the inner interval. The previous statements about what holds when Junior arrives in London should still seem ok. However, suppose we postulate that Junior spent time in Peking on the way from Glasgow to London. This would make the narrative anomalous, but some geograhical knowledge is required to make the anomaly apparent.