Exercise 14.5 Suppose that, in event calculus, there are two actions, Open and Close, and a relation opened that is initially, at time 0, false. Action Open makes opened true, and action Close makes opened false. Suppose that action Open occurs at time 5, and action Close occurs at time 10.

(a) Represent this in event calculus.

(b) Is opened true at time 3? Show the derivation.

(c) Is opened true at time 7? Show the derivation.

(d) Is opened true at time 13? Show the derivation.

(e) Is opened true at time 5? Explain.

(f) Is opened true at time 10? Explain.

(g) Suggest an alternative axiomatization for holds that has different behavior at times 5 and 10.

(h) Argue for one axiomatization as being more sensible than the other.