A Formal Semantics of Plural NPs

There is a widely accepted, through imprecise approach to semantics of plural NPs, based on the concept of "sums", which is from the traditional notion of "sets" in logic. It is believed that we recognize sums of things as a part of our ontology, while this does not necessarily occur in the case of sets. To account for the meaning of a plural NP, the above- mentioned model of interpretation considers sums of things directly. However, there has been another model which, by contrast, takes singular entities as part of sums. Both models represent just a totality of the referential function of the plural NPs. They can't make a distinction between distributive and collective readings or between existential and generic readings of plural NPs. This paper tries to draw the logical forms of the related sentences regarding various readings. We will see that plural NPs can refer to at least four types of sums. Moreover, reference to these types is not encoded semantically in the NPs themselves; it is mostly the result of the world- language interaction.