natural deduction metalanguage, practical foundations
type theory (dependent, intensional, observational type theory, homotopy type theory)
computational trinitarianism =
propositions as types +programs as proofs +relation type theory/category theory
In propositional logic, the contrapositive rule states that it is valid to derive from (where is negation and is implication). In symbols:
The combination of this rule, followed by modus ponens (the elimination rule for implication) was traditionally called modus tollens:
The contrapositive rule is valid in intuitionistic logic, not just in classical logic; however, the reverse rule is valid only in classical logic.
Another intuitionistically valid rule, this one reversible, is
as both statements are equivalent to the negation of (where is conjunction). However, the superficially similar
is again valid only classically.
Last revised on April 23, 2017 at 15:19:33. See the history of this page for a list of all contributions to it.