Axiomatics for implication.
David Meredith · Notre Dame Journal of Formal Logic · 1979
This paper presents a basic axiomatic and two increments thereto, for propositional systems with implication as the sole functor.The basic axiomatic gives exactly the set of Modus Ponens formulae (defined below); addition of the first increment gives Positive Logic; and with addition of the second increment we reach the complete Classical Logic.After some preliminaries in section 1, the axiomatics are presented in section 2. Section 3 establishes their properties.