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Fragments convey the same propositional content that their full sentential counterparts do. The form-function mismatch of fragments has been one of the non-trivial issues in syntax, semantic and pragmatics. We suggest that there are two types of fragments in English, and they have different derivational processes and interpretative mechanism. Case-marked fragments have full sentential structures prior to ellipsis and the interpretation follows from the sentential structures that are the sources of propositional interpretations. Caseless fragments, on the other hand, are base-generated nonsentential XPs whose interpretations come directly from pragmatics-discourse.