Filter is a particular type of generalized quantifier Q, (Q is not empty), which obeys condition (i) in a domain of entities E:
(i) for all X,Y subset E: (X in Q and Y in Q) <=> intersection(X,Y) in Q
All N, both N and the N are examples of filters, but some N and most N are not. This accounts for the contrast between (ii) and (iii):
(ii) All dogs bark and all dogs run <=> all dogs bark and run (iii) Some dogs bark and some dogs run <=/=> some dogs bark and run.
Device which only allows signals of certain frequencies to pass. Filtered speech can be used in perception experiments to study whether words can be recognised after certain frequencies have been removed.
- Zwarts, F. 1981. Negatief polaire uitdrukkingen, Glot 4, 35-132
- German Filter (de)