classical propositional logic

Definition

Classical propositional logic is that branch of propositional logic based on Aristotelian logic, with tenets:

1. A statement must be either true or false, and there can be no middle value (law of excluded middle)
2. A statement cannot be both true and not true at the same time, i.e. cannot contradict itself (principle of non-contradiction)

Notes

• Consider the formal language of propositional logic $\mathcal{L}_0$ which, endowed with deductive apparatus (axioms and rules of inference), is made into a formal system

References

1. https://proofwiki.org/wiki/Definition:Classical_Propositional_Logic
2. https://ncatlab.org/nlab/show/classical+logic