Representation of Defaults

In Active logic, defaults can be represented using default rules like (4.5), which states that if $\neg$P is not known at the current time, and if Q is known, then P is inferred by default at the next time step.

$${\tt i} : Q, \neg Know(\neg P,i), Now(i)$$

$$\cline{1-3} {\tt i+1} : P \nonumber$$

Since only a linear lookup in the belief set for time i is needed to tell that $\neg P$ is not there (and that $Q$ is there), the decidability issues of traditional default mechanisms do not arise in Active logic. The default rule in itself does not deal with problems arising from interacting defaults. However, since such cases tend to involve contradictory conclusions (as when, evidence for $\neg P$ becomes known), they can be treated as any other contradictands. One simple expedient in such cases is to disinherit the default conclusion and accept the non-default evidence.