# Cool Logic

Omer Korat (ILLC)

### Challenges for a Theory of Plurality

November 27th at 17:30, in ILLC Seminar Room (F1.15)

Different predicates give rise to different entailment patterns. For instance, (1) entails that every soldier cocked his rifle, but (2) doesn't seem to entail that every soldier conquered the fort: (1) The soldiers cocked their rifles. (2) The soldiers conquered the fort. (1) is an example of a distributive sentence, in which the predicate distributes down to the singular elements of its argument. (2) is an example of a collective sentence, in which the predicate applies to its argument collectively. Some predicates are ambiguous between distributive and collective readings, as in (3): (3) The soldiers raised a flag. To complicate things, in some cases two arguments of a predicate may be interpreted distributively, as Remko Scha's famous example (4). (4) can mean that each firm used at least one computer, and each computer was used by at least one firm. We call such readings cumulative. (4) 500 Dutch firms used 5000 American computers. Such readings are affected not only by the predicate, but also by the argument. For instance, while (3) is ambiguous between the collective and distributive reading, (5) has only the collective reading, because its subject is a group noun (rather than a plural noun). (5) The army raised a flag. In the talk I present various entailment patterns which emerge as a result of properties of nominal expressions, and describe several attempts to derive these patterns in an algebraic (mereological) framework. Finally, I demonstrate where these analyses fail, and what may be a possible solution.