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Up to now we have seen various ways to construct logical formulae as meaning representations for sentences. But we don't yet know what to do further with such formulae. We will now learn how to do useful work with meaning representations like the ones we saw being constructed in the last lectures.
If we utter a sentence, we transport information. One way of exploiting this information is to find out what follows from the sentence. The parallel task on the level of meaning representations is that of inference from the formula for that sentence. So it would be a great step forward if we could automate the process of drawing inferences from such formulae. For this purpose, one uses calculi known from theoretical logic. The method that we will discuss in this chapter at length is that of semantic tableaux. We start by discussing inference for a propositional logic, leaving the more complex issue of first order inference for later. In the next chapter, we will see that the Prolog implementation of propositional tableaux is straightforward.
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