Before discussing reasoning, we first briefly
address the problem of representation in the attributevalue
language. Reasoning tasks are often expressed
in English and have simple, direct counterparts in the
classical first-order logic language (FOL). For PDL2
to reason about such first-order statements, they must
first be translated into an equivalent symbolic-valued
attribute language (AVL) representation. Note
however that AVL is not as expressive as FOL, so that
only certain FOL statements can be translated directly
into AVL statements. Essentially, only implications
whose predicates all range over a single universally
quantified variable, and whose premise is a
conjunction of predicates may be translated. In some
cases, contextual information may be used to lift this
restriction. Despite said limitations, several
interesting commonsense reasoning protocols satisfy
AVL's requirement, and can thus be handled by PDL2.