In logic, as in grammar, a subject is what we make an assertion about, and a predicate is what we assert about the subject. We adopt the convention that subjects are symbolized by lower-case letters, and predicates by capitals. We also adopt the convention that predicates are put first and subjects second in our notational formulas. This course and this hand-out are limited to first order logic.
Variables are placeholders that range over individual objects.
Quantifiers tell us of how many objects the predicate is asserted. Hence, another name for predicate logic is quantification theory . With the two quantifiers and negation, we can express the three quantities, all , some , and none . Quantifiers refer to the universe of discourse , the background set of things we are talking about. By default, the universe of discourse contains everything whatsoever that can be referred to.