title: representation of context free grammar relations
body: <p>The production rules of a context free grammar are formalised as pairs, just a set of relations... </p>
  
  <pre><code>(α,β) ∈ R 
  </code></pre>
  
  <p>where <strong>α</strong> is a non-terminal and <strong>β</strong> is either a terminal or a non-terminal.</p>
  
  <p>thus S → A could be written as (S,A) ∈ R</p>
  
  <p>But when parsing tagged natural language trees for probabilitic CFG's. Many of there rules are of the form:</p>
  
  <pre><code>NP → NNP POS
  </code></pre>
  
  <p>that is, the right hand side is not <strong>always</strong> a single terminal or non-terminal</p>
  
  <p>Is there a way of formalising these production rules? As I can't see the relation method working...</p>
  
  <p>unless they were perhaps more like (NP → NNP) → POS</p>
  
  <p>Or is it that they are not the exact production rules, </p>