Logical derivations are structured proofs where each step follows logically from previous steps using inference rules.
Given: "If P then Q" (P→Q) and "P", you can conclude: Q
Given: "If P then Q" (P→Q) and "¬Q", you can conclude: ¬P
Given: "P→Q" and "Q→R", you can conclude: P→R
Given: "P∨Q" and "¬P", you can conclude: Q
Beyond Propositional Logic
Predicate logic analyzes the structure within statements using quantifiers. This allows us to express arguments that propositional logic cannot capture.
All humans are mortal. ∀x(Hx → Mx)
Socrates is human. Hs
Therefore, Socrates is mortal. Ms
Modal logic introduces notions like necessity and possibility, letting us argue about what must or might be the case.
Necessarily, if the light is red then you must stop. □(R → S)