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.”