Propositional logic

Propositional logic is a formal system in mathematics and logic. Other names for the system are propositional calculus and sentential calculus. The system is made of a set of propositions. Each proposition has a truth value, being either true or false. Propositions can be represented by capital roman letters such as ${\displaystyle P}$, ${\displaystyle Q}$ and ${\displaystyle R}$, and joined together using logical connectives to make new propositions. Examples for logical connectives that are used often are logical and (${\displaystyle \land }$), logical or (${\displaystyle \lor }$), logical if (${\displaystyle \rightarrow }$), logical if and only if (${\displaystyle \leftrightarrow }$) and logical not (${\displaystyle \lnot }$).^[1][2]

Propositional logic only looks at the propositions and how they are connected, and does not decompose them.^[3] That way, the proposition All cats are dogs and the earth is a disc is made of two propositions, All cats are dogs, and The Earth is a disc. These are joined together with the logical connective AND.

There are other logic systems that build on propositional logic. One of these is predicate logic, which defines logical predicates, and looks at how they can be applied to arguments. Another system is called modal logic. It introduces two new junctors: it is possible that and it is necessary that.

1. ↑ "Comprehensive List of Logic Symbols". Math Vault. 2020-04-06. Retrieved 2020-08-20.
2. ↑ "Propositional Logic | Brilliant Math & Science Wiki". brilliant.org. Retrieved 2020-08-20.
3. ↑ "Propositional Logic | Internet Encyclopedia of Philosophy". Retrieved 2020-08-20.