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7. Counterfactual conditions:
If John had married Mary, his life would have been happier presupposes that John didn't marry Mary.
8. Temporal clauses:
Before he came, the party was over presupposes that He came.
9. Nonrestrictive relative clauses:
The man who is living next door is your father presupposes that A man is living next door.
These phenomena are the most typically defined as presuppositions within linguistic theory. However, it should be pointed out that any delimitation of the domain of presuppositional phenomena depends strictly on the definition of presupposition one uses. Thus there is not absolute agreement on the list above; some of the preceding cases are excluded by some authors, whereas some others are added.
Given the nonhomogeneous nature of these phenomena, it seems reasonable to challenge a rigid notion of presupposition, which is more an artifact of linguistic theory (Dinsmore 1981a) than a specific feature of linguistic expression. As Karttunen and Peters (1979) say, a wide range of different things have been lumped together under this single label and this fact is responsible for the continuing controversy about how to analyze presuppositions.
Our aim is to sketch the general lines along which the presupposition problem should be framed, and then to analyze more specifically some of the phenomena listed above. In order to do that, we have to consider briefly the different theories under which presuppositions have been studied so far. Basically, they can be classified in two main approaches: semantic and pragmatic. Both of them seem to be inadequate to account fully for our intuition of presuppositional phenomena.
The semantic theory of presupposition is committed to a truth-functional approach, concerned with the logical conditions under which a presupposition can be introduced into a true sentence. The basic hypothesis of this paper is that such a truth-functional approach cannot capture presuppositional phenomena as they occur in actual processes of communication based on a natural language.
From a pragmatic point of view, different explanations have been proposed to explain presuppositions. Two basic concepts are involved:

 
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