In order to carry out this transformation, equivalences such as the following are utilised. If several disjuncts satisfy the oldest, we choose between these on the basis of the next oldest. And so on. If several disjuncts satisfy exactly the same eventualities, the choice becomes non-deterministic. If a contradiction is encountered, i.e. all the 's are inconsistent, then backtracking is invoked.
Execution returns to a previous choice point and an alternative disjunct is chosen.
If all possible disjuncts have been tried, the execution fails. There are two approaches used to avoid this. Once the same state has been constructed a number of times, with the same eventualities outstanding, a theorem-prover can be invoked to check whether the current sequence can possibly lead to successful execution. As theorem-proving can be expensive, an alternative is to utilise the fact that the logic has the finite model property, as follows. Let be Then, a structure containing all possible models can be constructed with at most states.