Sometimes we name what we want to talk about with letters: person S, belief p, intention N. Should we use any article for them? Definite names are never used with articles. For me the ambiguity here is on whether something named with a letter is a definite name so that it doesn't need any article neither in the first usage nor in the subsequent ones.
Suppose, for instance, that person S forms belief p.
Suppose, for instance, that the person S forms the belief p.
Suppose, for instance, that a person S forms a belief p.
What about the subsequent usages?