  A given question can be defined in terms of the set of statements or
assertions that answer it. Application of logical inference to these sets of
assertions allows one to derive the logic of inquiry among questions. There are
interesting symmetries between the logics of inference and inquiry; where
probability describes the degree to which a premise implies an assertion, there
exists an analogous measure that describes the bearing or relevance that a
question has on an outstanding issue. These have been extended to suggest that
the logic of inquiry results in functional relationships analogous to, although
more general than, those found in information theory.
  Employing lattice theory, I examine in greater detail the structure of the
space of assertions and questions demonstrating that the symmetries between the
logical relations in each of the spaces derive directly from the lattice
structure. Furthermore, I show that while symmetries between the spaces exist,
the two lattices are not isomorphic. The lattice of assertions is described by
a Boolean lattice 2^N, whereas the lattice of assuredly real questions is shown
to be a sublattice of the free distributive lattice 2^(2^N). Thus there does
not exist a one-to-one mapping of assertions to questions, there is no
reflection symmetry between the two spaces, and questions in general do not
possess complements. Last, with these lattice structures in mind, I discuss the
relationship between probability, relevance, and entropy.
