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The semantic interpretation of progressive accomplishments is thought to be notoriously hard because of the "imperfective paradox," and appears to require a modal treatment. In the first part of the paper we describe a clear-cut scenario in which two of the most influential modal theories, Dowty (1979) and Landman (1992), give the wrong prediction, and we also present a challenge that highlights an explanatory deficiency of these theories. In the second part of the paper, we develop a general mereology-based framework which contains, as a special case, a theory of the
progressive. The framework utilizes a particular type of connection, called a Galois connection, between the properties of the parts of an entity and the properties of the entity itself. As we show in the last part of the paper, this framework avoids the problems discussed in the first part, and provides a non-modal theory for the progressive.
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