Proofs of all theorems are provided in the appendix.
Theorems 1 and 2 say that the PIGC characterizes the indefiniteness of an
IDDB.
That is, it seems unavoidable to consider PIGC in some form or other
for answering Indef[A] and False[A]. However, since it is obviously infeasible
to derive PIGC in general, we should develop an appropriate mechanism to
handle only PIGC[A], that is, the portion of PIGC relevant to the atom being
evaluated.
Compilation
and
Representation
Alternatives
In this section, we introduce the two important
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