I consider first the pure implicational fragments of E , R and T . E has the structure of modalities close to that of S4 . It turns out that Self-Implication being the archetypal form of inference leads to certain fallacies of relevance. Though systems of relevance logic are freed from paradoxes still some of them remain. K R strengthens K E and identifies arbitrary theorem with Self-Implication .
T is really free from such fallacies.
Another problem arises in the context of entailment with negation. The third defect of current relevance logic is connected with its incompleteness in intuitive sense. If we add to any of the systems discussed above one of them, a new bulk of interesting systems arises. A good deal of light can be shed on the foundations of the systems of relevance logic by considering entailment relation in terms of information theory. The clear and close relationship of the concepts of information and entailment was found out by E.Voishvillo.