On some neglected paradoxes of modern logic

A four-valued truth-functional logic is presented. Among the specific features of the logic is a similarity to PROLOG and also to intuitionism. The logic is machine hardware representable by means of greater and lesser voltages or by means of a two-wire scheme. Without sacrificing truth functionality, without introducing modal operators, without making relevance a precondition for reasoning, without any gimmicks of unorthodoxies, and without any untoward consequences, one can avoid various paradoxes of standard logic. The initial focus is on two paradoxes. The first is that denying a conditional statement implies affirming its antecedent. The second is that ~[p⟨=⟩q] implies [p x-or q], and that ~[p x-or q] implies [p⟨=⟩q]. The author shows that the first paradox can be avoided. Then, he develops several different varieties of equivalence and mutual exclusivity, and dispel the second paradox. Finally he considers some new issues, focusing on whether or not [~(p=⟩q) and (r=⟩q)] implies [~r]. This proposition is a theorem both of standard logic and of his own system. Consequently, his main aim is to show that this proposition is unobjectionable