3 House Plumbing

In this example constants p1, p2 and p3 denote cold water pipes. Constants t1, t2 and t3 denote taps and d1, d2 and d3 denote drainage pipes. The constants shower denotes a shower, bath denotes a bath, sink denotes a sink and floor denotes the floor. The diagram above is intended to give the denotation for the symbols. Suppose we have as predicate symbols:

• pressurised, where pressurised(P) is true if pipe P has mains pressure in it.
• on, where on(T) is true if tap T is on.
• off, where off(T) is true if tap T is off.
• wet, where wet(B) is true if B is wet.
• flow, where flow(P) is true if water is flowing through P.
• plugged, where plugged(S) is true if S is either a sink or a bath and has the plug in.
• unplugged, where unplugged(S) is true if S is either a sink or a bath and has the plug in.

1. Finish the axiomatization for the sink in the same manner as the axiomatization for the bath. Test it in CILog.
2. Axiomatize how the floor is wet if the sink overflows or the bath overflows. They overflow if the plug is in and water is flowing in. You may invent new predicates as long as you give their intended interpretation. [Assume that the taps and plugs have been in the same positions for one hour; you don't need to axiomatize the dynamics of the turning on taps and inserting and removing plugs.] Test it in CILog.
3. Suppose there is a hot water system is installed to the left of tap t1. This has another tap in the pipe leading into it, and supplies hot water to the shower and the sink (there are separate hot and cold water taps for each). Add this to your axiomatization. Give the denotation for all constants and predicate symbols you invent. Test it in CILog.