1. Logical Statements


Propositional logic involves only declarative statements.

Complex propositions can be constructed by simple ones using operators.

<aside> 💡 p : "If the train is late and there are no taxis in the station, then Bob is late to work."

</aside>

We can examine whether such propositions are true or false when we know the values of the basic propositions.

English (or any human language) is imprecise and subtle (verb tenses, etc.) and error-prone. A more mathematical language for logic would make the above arguments clear (Propositional Logic).

2**. Symbolic Propositional Logical**


3**. Syntax**


To be rigorous, we need to define grammar (or meta-) variables that stand for any term derivable from the grammar: $A,B,...$

Definition The logical formulas of Propositional Logic are exactly those accepted by the following grammar in Backus Naur Form (BNF):

$$A::=p | (¬A) | (A∧A) | (A∨A) | (A→A)$$