This paper aims to integrate logical operators into frame-based semantics. Frames are semantic graphs that allow lexical meaning to be captured in a fine-grained way but that do not come with a natural way to integrate logical operators such as quantifiers. The approach we propose stems from the observation that modal logic is a powerful tool for describing relational structures, including frames. We use its hybrid logic extension in order to incorporate quantification and thereby allow for inference and reasoning. We integrate our approach into a type theoretic compositional semantics, formulated within Abstract Categorial Grammars. We also show how the key ingredients of hybrid logic, nominals and binders, can be used to model semantic coercion, such as the one induced by the "begin" predicate. In order to illustrate the effectiveness of the proposed syntax-semantics interface, all the examples can be run and tested with the Abstract Categorial Grammar development toolkit.
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