Formal language of propositional logic

In these notes, we will use the following symbols for the propositional calculus. Note some of these might not exist, depending on the logic used.

Precedence	Natural language	Name	Symbol
1	not $𝑝$	negation	$\neg 𝑝$
2	$𝑝$ and $𝑞$	conjunction	$𝑝 \land 𝑞$
3	$𝑝$ or $𝑞$	disjunction	$𝑝 \lor 𝑞$
4	$𝑝$ implies $𝑞$	implication	$𝑝 \Rightarrow 𝑞$
5	$𝑝$ iff $𝑞$	logical equivalence	$𝑝 \Leftrightarrow 𝑞$
-	tautology	tautology	$⊤$
-	falsum	falsum	$⊥$

𝜙 : : = 𝑝 ∣ \neg 𝜙 ∣ ⊤ ∣ ⊥ ∣ 𝜙 \land 𝜓 ∣ 𝜙 \lor 𝜓 ∣ 𝜙 \Rightarrow 𝜓 ∣ 𝜙 \Leftrightarrow 𝜓

We typically use square brackets $[-]$ as delimiters of propositions.

#state/tidy | #lang/en | #SemBr