The aim of logic in computer science is to develop languages to model the situations we encounter as computer science professionals, in such a way that we can reason about them formally. Reasoning about situations means constructing arguments about them; we want to do this formally, so that the arguments are valid and can be defended rigorously, or executed on a machine.
Consider the following argument:
Example 1.1 If the train arrives late and there are no taxis at the station, then John is late for his meeting. John is not late for his meeting. The train did arrive late. Therefore, there were taxis at the station.
Intuitively, the argument is valid, since if we put the first sentence and the third sentence together, they tell us that if there are no taxis, then John will be late. The second sentence tells us that he was not late, so it must be the case that there were taxis.
Much of this book will be concerned with arguments that have this structure, namely, that consist of a number of sentences followed by the word ‘therefore’ and then another sentence. The argument is valid if the sentence after the ‘therefore’ logically follows from the sentences before it. Exactly what we mean by ‘follows from’ is the subject of this chapter and the next one.
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