ABSTRACT

This chapter focuses attention upon the relation of tautological implication. It provides a minimal kit for basic work on systems of logic. Every case of tautological implication can be derived, in a short or a long time, from the chosen axioms by means of the chosen rules. Each axiom scheme and derivation rule is a well known personality in logical life. The topmost schemes tell us that a conjunction implies each of its conjuncts, and that a disjunction is implied by each of its disjuncts. Each axiom contains a single arrow, flanked on left and right by formulae. This arrow should not be conflated with the hook sign. There is nothing objectionable about these distribution principles, and they all correspond to genuine tautological implications.