### Modal Subordination in Type Theoretic Dynamic Logic

#### Abstract

Classical 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 subordi- nation. The theoretical backbone of the current work is Type Theo- retic Dynamic Logic (TTDL), which is a Montagovian account of dis- course 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 con-

versation 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 be- tween Modal-TTDL and TTDL will be discussed as well.

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