*Prologue*: To borrow straight out of [SEP][1]:

> The moon is made of green cheese.
> Therefore, either it is raining in
> Ecuador now or it is not.

In order to prevent explosion relevant logic is introduced which has prompted Anderson and Belnap's magnum opus *Entailment* (1975).  

As the example below from SEP shows:

$ 1. A_{\{1\}}$	  Hyp 

$ 2. (A → B)_{\{2\}} $ Hyp 

$ 3. B_{\{1,2\}} $    1,2, → E 

Now to prevent irrelevant premises "to creep in" Anderson and Belnap introduced the following rule:

From $A_{\{i\}}$ and $B_{\{i\}}$ to infer $(A\&B)_{i}.$ 

where *i* is the index and,

> This rule says that two formulae to be conjoined must have the same index before the rule of conjunction introduction can be used.

*My Question*: As an undergraduate before tackling the mammoth two part editions of the authors I am curious as to the juicy synopsis of their work. How does **R** actually resolve the entailment paradox with introduction of index because superficially it seems that it must work under assumption of $\mathbb{N}$ to use for index when $\mathbb{N}$ itself must be constructed from primitive recursion using entailment operator?

Intuitively it seems that there must be a hidden tautology inside somewhere. How can I see the big picture or a bit more precisely, how is entailment defined formally?

Thank you.

  [1]: http://plato.stanford.edu/entries/logic-relevance/