There exists x such that P(x,y) for any y in Y. For all x in X, there exists y such that P(x,y). There exists x in X such that P(x,y) for some y in Y. For all x in X, P(x,y) for all y in Y.

Definition [Positive Normal Form (release PNF)]For a ∈ AP, LTL formulae in release positive normal form (release PNF, or simply PNF) are given by ϕ ::= true | false | a | ¬a | ϕ ∧ ϕ | ϕ ∨ ϕ | ○ϕ | ϕ U ϕ | ϕ R ϕ

from : http://en.wikipedia.org/wiki/Formal_system In formal logic, a formal system (also called a logical system,[1] a logistic system,[1] a logical calculus,[2] or simply a logic[1]) consists of a formal language together with a deductive…