# Plural logic

**Plural logic** is logic that permits **plural quantification**, i.e., allows for variables to also take on plural values, such as “*x* = the cat and the dog (together)”, or “*y* = all of the students”.

Often, to drive this point home, the variables will be named like *xx* and *yy*.

Modeling language with plural quantification allows for expressing things like “the students work together” or “the students surround the building” without needing to involve cumbersome “sets” or “masses” of students: we can simply speak of the students acting as a plural entity.

(Singular logic, on the other hand, needs such constructs, or else you'll likely end up saying “for each student *x*: *x* surrounds the building”, which is semantically incorrect as “surrounding the building” is not distributive.)

Toaq is based on such logic:

- When you say sá poq, the domain ranged over by the variable póq is not only that of each individual person, but of all “people-s”, including all pairs and triples and groups of people. (If this is undesirable, there's sá shı poq, which only ranges over singular values. See Quantifier.)
- Numbers in Toaq have definitions like “saq: ___ (plural) are three in number.”

## See also

*Plural Predication*, a pretty cool book on this topic.- Plural quantification on Wikipedia.