Formal Definition of PCFGs
A PCFG consists of:
- A set of terminals, {wk}, k= 1,…,V
- A set of nonterminals, Ni, i= 1,…, n
- A designated start symbol N1
- A set of rules, {Ni --> ?j}, (where ?j is a sequence of terminals and nonterminals)
- A corresponding set of probabilities on rules such that: ?i ?j P(Ni --> ?j) = 1
The probability of a sentence (according to grammar G) is given by:
. P(w1m, t) where t is a parse tree of the sentence
. = ?{t: yield(t)=w1m} P(t)