The main question we investigate is whether meaning representations of the kind that are pervasive in formal semantics are built up incrementally and predictively when language is used in real time, in much the same way that the real-time construction of syntactic representations has been argued to be. The interaction of presupposition resolution with conjunctions vs. conditionals with a sentence-final antecedent promises to provide us with the right kind of evidence. Consider the following 'cataphoric' example and the contrast between "and" and "if": "Tina will have coffee with Alex again and / if she had coffee with him at the local cafe". We expect the second clause to be more difficult after "and" than after "if": the conjunction "and" signals that an antecedent that could resolve the "again" presupposition is unlikely to come after this point (the second conjunct is interpreted relative to the context provided by the first conjunct), while the conditional "if" leaves open the possibility that a suitable resolution for the "again" presupposition is forthcoming (the first clause is interpreted relative to the context provided by the second clause). We present experimental evidence supporting these predictions and discuss two approaches to analyze this kind of data.