  The founder of modal logic, C. I. Lewis, defined a series of modal logics which did not have \(\Box\) as a primitive symbol. Lewis was concerned to develop a logic of conditionals that was free of the so called Paradoxes of Material Implication, namely the classical theorems \(A\rightarrow({\sim}A\rightarrow B)\) and \(B\rightarrow(A\rightarrow B)\). He introduced the symbol \(\fishhook\) for “strict implication” and developed logics where neither \(A\fishhook ({\sim}A\fishhook B)\) nor \(B\fishhook (A\fishhook B)\) is provable. The modern practice has been to define \(A\fishhook B\) by \(\Box(A\rightarrow B)\), and use modal logics governing \(\Box\) to obtain similar results. However, the provability of such formulas as \((A \amp{\sim}A)\fishhook B\) in such logics seems at odds with concern for the paradoxes. Anderson and Belnap (1975) have developed systems \(\mathbf{R}\) (for Relevance Logic) and \(\mathbf{E}\) (for Entailment) which are designed to overcome such difficulties. These systems require revision of the standard systems of propositional logic. (See Mares (2004) and the entry on  relevance logic.)