5.1.4 The Fifth Reading
Continuation.
Two readings may be equivalent...
If you have already looked closely at all the readings we have listed for the complex example, you will have noticed that the fourth and fifth readings are logically equivalent.
Exercise 5.6
Give a natural language paraphrase for the fifth reading and compare it to the paraphrase for the fourth one. Can you explain why both readings are equivalent by examining the corresponding formulas?
...but not necessarily
The reason why we have listed readings four and five separately in spite of this is that there are structurally identical examples (which just use other determiners) in which the two readings do mean different things. Consider the sentence ``Every researcher of a company saw most samples.'' Because of the determiner "most", the readings of this sentence can't be represented in first-order logic, but we can use 
as the analogue of 
and 
in the 
terms. We are then able to write the semantic representations of the fourth (1.) and fifth (2.) reading of the previous example as follows:
Exercise 5.7
Do you see the difference (in meaning) between the two readings? Give a natural language paraphrase for each of the readings and try to think of contexts that would favour one or the other. Can you explain why the ordering of the representations of the two determiners
and
makes a difference in this case (in contrast to the corresponding determiners in our siamese-cat-example)?