Situation calculus theories are somewhat similar to celestial mechanics in the kinds of counterfactuals they admit. However, different situation calculus formalizations of the same phenomenon may admit different counterfactuals.

Consider two similar theories, the Yale Shooting Problem with the additional statement what walking implies being alive, and the Yale Shooting Problem with the additional rule that shooting causes someone to stop walking (when the gun is loaded). These theories are equivalent when we add induction, as the domain constraint can be derived by an induction.

We now consider what might happen if the gun was a pellet gun. Pellet guns wounds, though painful are not fatal. Thus, we remove the effect axiom that states shooting kills. In one case, we are left with the effect axiom that shooting stops someone walking, even though it does not kill them--a reasonable conclusion. In the other, we are left with no effects, as the second effect axiom was a consequence of the domain constraint and the axiom that shooting kills.

Thus how we axiomatize our theory can alter the truth of counterfactuals.

Wed Jul 12 14:10:43 PDT 2000