Adnominal genitives and prepositional phrases (PPs) have a wide range of interpretations. For instance, they may be interpreted as arguments of an event nominalization or a relational noun. They may also express possession or some general associative relation, cf. the German Determiner Phrases

Phenomena such as logical polysemy and logical metonymy have recently received a precise treat-ment by using a rich composition logic that assumes complex types and rich introduction and exploita-tion rules for manipulating them (Asher and Puste-jovsky, 2005). An interesting question is whether this approach can be extended and applied to other lexical semantics phenomena, in particular to con-trastive ambiguity (aka homonymy). This paper en-riches Asher and Pustejovsky’s Type Composition Logic with another type of complex types, namely disjunctive types, and accompanying exploitation and introduction rules to model homonymy. This results both in a more elegant and economical treat-ment of homonymy and in a more general account of lexical ambiguity. 1