In many of the abstract geometric models which have been used to
represent concepts and their relationships, regions possessing some
cohesive property such as convexity or linearity have played a
significant role. When the implication or containment relationship is
used as an ordering relationship in such models, this gives rise to
logical operators for which the disjunction of two concepts is often
larger than the set union obtained in Boolean models. This paper
describes some of the characteristic properties of such broad
non-distributive composition operations, which are related to the
traditional inductive hypotheses of learning algorithms. The lattice
of subspaces of a vector space is presented as a special example, in
which the subspace lattice is formally related to the tensor algebra,
used already for composition in quantum mechanics and Holographic
Reduced Representations.