AbstractClassical theories of discourse semantics, such as Discourse Representation Theory (DRT), Dynamic Predicate Logic (DPL), predict that an indefinite noun phrase cannot serve as antecedent for an anaphor if the noun phrase is, but the anaphor is not, in the scope of a modal expression. However, this prediction meets with counterexamples. The phenomenon modal subordination is one of them. In general, modal subordination is concerned with more than two modalities, where the modality in subsequent sentences is interpreted in a context ‘subordinate’ to the one created by the first modal expression. In other words, subsequent sentences are interpreted as being conditional on the scenario introduced in the first sentence. One consequence is that the anaphoric potential of indefinites may extend beyond the standard limits of accessibility constraints. This paper aims to give a formal interpretation on modal subordination. The theoretical backbone of the current work is Type Theoretic Dynamic Logic (TTDL), which is a Montagovian account of discourse semantics. Different from other dynamic theories, TTDL was built on classical mathematical and logical tools, such as λ-calculus and Church’s theory of types. Hence it is completely compositional and does not suffer from the destructive assignment problem. We will review the basic set-up of TTDL and then present Kratzer’s theory on natural language modality. After that, by integrating the notion of conversation background, in particular, the modal base usage, we offer an extension of TTDL (called Modal-TTDL, or M-TTDL in short) which properly deals with anaphora across modality. The formal relation between Modal-TTDL and TTDL will be discussed as well. We uncover the difficulty of specific sense distinctions by investigating distributional bias and reducing the sparsity of existing small-scale corpora used in prior work. We build a semantically enriched model for modal sense classification by designing novel features related to lexical, proposition-level and discourse-level semantic factors. Besides improved classification performance, closer examination of interpretable feature sets unveils relevant semantic and contextual factors in modal sense classification. Finally, we investigate genre effects on modal sense distribution and how they affect classification performance. Our investigations uncover the difficulty of specific sense distinctions and how they are affected by training set size and distributional bias. Our large-scale experiments confirm that semantically enriched models outperform models built on shallow feature sets. Cross-genre experiments shed light on differences in sense distributions across genres and confirm that semantically enriched models have high generalization capacity, especially in unstable distributional settings.