  Given appropriate representations of the semantic relations between carpenter
and wood and between mason and stone (for example, vectors in a vector space
model), a suitable algorithm should be able to recognize that these relations
are highly similar (carpenter is to wood as mason is to stone; the relations
are analogous). Likewise, with representations of dog, house, and kennel, an
algorithm should be able to recognize that the semantic composition of dog and
house, dog house, is highly similar to kennel (dog house and kennel are
synonymous). It seems that these two tasks, recognizing relations and
compositions, are closely connected. However, up to now, the best models for
relations are significantly different from the best models for compositions. In
this paper, we introduce a dual-space model that unifies these two tasks. This
model matches the performance of the best previous models for relations and
compositions. The dual-space model consists of a space for measuring domain
similarity and a space for measuring function similarity. Carpenter and wood
share the same domain, the domain of carpentry. Mason and stone share the same
domain, the domain of masonry. Carpenter and mason share the same function, the
function of artisans. Wood and stone share the same function, the function of
materials. In the composition dog house, kennel has some domain overlap with
both dog and house (the domains of pets and buildings). The function of kennel
is similar to the function of house (the function of shelters). By combining
domain and function similarities in various ways, we can model relations,
compositions, and other aspects of semantics.
