Logical Symbols

Primitive Logical Symbols

(,) parentheses, $v_0,v_1,v_2,...$ variable symbols (usually just called variables), connection: $\neg$ not, $\wedge$ and, quantifier: $\forall$ for all, binary symbol: $=$ equal

we can define other logical symbols through the primitive ones:

Definition

or: $\phi \vee \psi$ for $\neg (\neg \phi \wedge \neg \psi )$ implies: $\phi \to \psi$ for $\neg (\phi \wedge \neg \psi )$ if and only if: $\phi \leftrightarrow \psi$ for $(\phi \to \psi )\wedge (\psi \to \phi )$ there exists: $\exists v\phi$ for $\neg \forall v\neg \phi$