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If a cluster of messages does not satisfy within a given scope, it may satisfy in a larger scope. Therefore, if none of the messages are satisfiable together with a given scope or the user of this tool wants to see if the world view could be any different, then the user may re-run Alloy Analyzer on the same set of predicates by increasing the scope of the variables. However, these newly created world views may get less priority as they are likely to produce more ambiguous pictures of a situation. Consider the following three messages as an example:

1. “There is a collision between two cars” [Minimum Scope: 1 Person, 2 Cars] 2. “Head-on collision between two cars” [Minimum Scope: 2 Persons, 2 Cars] 3. “Man died as a car crashed on motorbike” [Minimum Scope: 1 Person, 1 Car,

1 Motorbike] (We are not certain that this car is not one of the cars stated in earlier messages)

The first two messages satisfy together and form a world view with only two men and two cars in the universe. If we increase the scope, all three messages will satisfy together and will form a bigger world view with only two men and two vehicles instead of two cars in the universe (as we are not certain that the car mentioned in the last message is not one of the cars stated in earlier messages). But this bigger world view gives a less conclusive message and is more ambiguous as there can be multiple possibilities of collisions between different vehicles. Therefore, this world view may be less dependable/credible. However, if the user is somehow convinced, for example, that there is more than one incident at a certain place then s/he may increase the scope without diminishing the credibility of the new world view. Also, in the case that the car mentioned in the third message was somehow uniquely identified and is one of the cars mentioned in message one and message two, the third message may be taken into the world view along with the first two without diminishing the credibility of the new world view. Also, smaller scope may not always produce a good result as two different incidents may appear as one incident with a smaller scope.

7.4.3

Impact of a new message on existing world views

Before explaining the impact of a new message on existing world views, it is impor- tant to describe the procedure of generating world views by incorporating the new

message. This will make it easier to understand the impact.

Procedure of incorporating a new message

Instead of trying to create world views by combining the newly received message with all existing messages, the new message will be combined with each of the exist- ing world views only. This will save the processing time by avoiding the repetition of the satisfiability checking of the same clusters that have already been checked before the existing world views were generated. The rest of the procedure will remain the same as that of creating the initial world views i.e. split them only when the new clusters do not satisfy. This whole process can be illustrated with an example shown

Figure 7.16: Combine a New Message with Existing World Views

in Figure 7.16. Suppose we have five messages A, B, C, D,and E and three world views namely ACDE, ABC and BE. Later, we have received a new message M. Instead of initiating the process of creating world views with the message cluster

ABCDEM and downsizing it as necessary, we will start with clusters ACDEM, ABCM and BEM. We will repeat the same procedure (described earlier) of split- ting them into smaller clusters if they are not consistent. Suppose at the end of the

process we have found three more world views namely ACM, DM and BEM in addition to the existing world views. Since the newly found world view BEM is a superset of the already existing world view BE and only the largest, unique and consistent sets of messages form world views, I will not considerBEas a world view any more.

Result of incorporating a new message

When a new message is incorporated into the existing set of messages and world views, one or more of the following cases will arise:

1. None of the existing world views are consistent with the new message. 2. All of the existing world views are consistent with the new message.

3. Some of the existing world views are consistent with the new message and some are not. Those world views that are not consistent with the new message will lead to either of the following cases:

(a) None of their factors/subsets are consistent with the new message. (b) Some of their factors/subsets are consistent with the new message. Depending on which of the above cases hold when a new message is incorporated into the existing set of messages and world views, either of the following things will happen to the existing world views:

• In Case-1, all of the existing world views will remain unchanged and the new message will be treated as a separate world view on its own. Hence the number of world views will remain the same except the new ‘singleton’ world view.

• In Case-2, a new larger world view will be produced from each of the existing world views but the number of world views will remain the same.

• In Case-3, the number of world views will certainly increase because a new larger world view will be produced from each of the (existing) world views that are consistent with the new message, while the rest of the world views that are inconsistent with the new message will produce either of the two results:

a) No new world views will be generated as none of the factors/subsets of the (existing) world view are consistent with the new message. However, the original world views will be retained.

b) One or more new but smaller world views will be generated (from one of the factors/subsets of the original world view are consistent with the new message) while the original world views will be retained.