Propositional calculus
Semantic truth, validity, consequence

Given φ {\displaystyle \varphi } and ψ {\displaystyle \psi } as formulas (or sentences) of a language L {\displaystyle {\mathcal {L}}}, and I {\displaystyle {\mathcal {I}}} as an interpretation (or case) of L {\displaystyle {\mathcal {L}}}, then the following definitions apply:

For interpretations (cases) I {\displaystyle {\mathcal {I}}} of L {\displaystyle {\mathcal {L}}}, these definitions are sometimes given:

For classical logic, which assumes that all cases are complete and consistent, the following theorems apply:
detectable_content:number_placeholders[3], change_case:capital_word_frequency[4]