cross-linguistic studies of polysemy?

[Chris Sinha]

Some form classes are more susceptible to polysemy than others
(prepositions more so than nouns, for example), so that typological
differences could affect the overall frequency of polysemous items.
But polysemy is a tricky issue anyway and it can be more useful to
look at the distribution of meaning across form classes, both
systemically and syntagmatically. With respect to the domain of
space, Sinha and Kuteva advance the following hypotheses on the basis
of the distributed semantics analysis:

H:  Languages which largely restrict the overt expression of spatial
relational meaning to a single form class of locative particles
willbe characterizable in terms both of relatively high (but also
relatively discrete) polysemy of items in this class, and of complex
and non-compositional covert distribution of expression of spatial
relational meaning across co-present open class items. Such languages
will in general disfavour optionality in the expression of spatial
relational meaning through the locative particle system, but will
favour it in contexts where open class items explicitly (overtly)
express spatial relational meaning. These languages will also
disfavour the overt repetition of the same spatial relational meaning
at different points in the syntagmatic string.

H2: Languages which overtly distribute spatial relational meaning
across co-selections from two or more closed classes may exhibit high
degress of polysemy (in the limit case, extreme meaning
indeterminacy) in one or more of such classes, but will compesate by
high specificity of meaning in other closed classes; and such
languages will favour both the contextually-determined optionality of
some spatial relational meaning-bearing items, and the overt
repetition within a single syntagmatic string of the same spatial
relational information.

C. Sinha and T. Kuteva (1995)  Distributed spatial semantics. Nordic
Journal of Linguistics, 18, 167-199.

(Note: a language of the type characterized in H1 is English; a
language of the type characterized in H2 is Japanese. English having
a "covertly" distributed spatial semantics, and high but discrete
"overt"  lexical polysemy in prepositions, and Japanese having an
overtly distributed spatial semantics, "bleaching"-type polysemy on
postpositions, strong specification of path and disposition in
verbs, and locative nouns which are less polysemous than English
prepositions.)

Chris Sinha