Introduction to Philosophy/Logic/Fault Diagnosis
Our propositional calculus can be quite useful for descriptions of systems and fault diagnoses. Here are some propositions regarding part of a fairly simple plumbing system:
- If there is an overflow in the upper tank, then the buzzer is sounding or there is an electrical problem.
- If there is water dripping from the ceiling, then there is an overflow in the upper tank.
- The buzzer is not sounding.
- There is water dripping from the ceiling.
- There is an electrical problem.
As with many things the propositions could be divided into:
- observations, e.g. 'the buzzer is sounding';
- hypothetical if-then statements;
Anyway, to show that the argument above is valid, we first assign letters to all the elementary propositions:
- p - there is an overflow in the upper tank;
- q - the buzzer is sounding;
- r - there is an electrical problem;
- s - water is dripping from the ceiling.
Then we can write our propositions out using symbols:
- P → (q ∨ r)
- s → p
- ¬ q
With fairly simple systems, one's intuition usually provides the correct answer fairly quickly. If you think of a chemical plant or a power station, the chains of inference can get quite complicated, yet swift action may be required in the case of a fault. In this case automated reasoning in the form of 'expert systems' can be quite useful. (Of course then there is the problem that the expert system could be faulty. Here we encounter the problem of infinite regress.) When the reasoning gets complicated, the kind of analysis we have done here becomes useful.
If this kind of thing interests you, then perhaps you should study artificial intelligence.