Q:

representation of context free grammar relations

The production rules of a context free grammar are formalised as pairs, just a set of relations... 
(α,β) ∈ R 

where α is a non-terminal and β is either a terminal or a non-terminal.
thus S → A could be written as (S,A) ∈ R
But when parsing tagged natural language trees for probabilitic CFG's. Many of there rules are of the form:
NP → NNP POS

that is, the right hand side is not always a single terminal or non-terminal
Is there a way of formalising these production rules? As I can't see the relation method working...
unless they were perhaps more like (NP → NNP) → POS
Or is it that they are not the exact production rules, 

A:

A context-free grammar is defined by a four-tuple (V, T, P, S):

V   a set of non-terminal symbols
T   a set of terminal symbols, disjoint from V
P   a set of productions, each of which is a mapping v → ω where v ∈ V and ω ∈ (V &Union T)*
S   an element of V, the start symbol

Technically, you could derive V and T from P. However, everyone does roughly as above (with some variation of names, and occasionally using V and V &Union T as primitives instead of V and T).
The important point (in bold above) is that the right-hand side of a production is not "a terminal or a non-terminal" but rather "an element of (V &Union T)*". If you couldn't expand a non-terminal into more than one symbol, your language would only consist of single-element strings.

