This file formalizes Degano and Aloni's typology of marked indefinites. An indefinite
has three uses, specific known, specific unknown and non-specific, and a marked indefinite is
restricted to some of them: of the seven possible restrictions, six are attested and the one
covering the specific known and the non-specific use without the specific unknown is not. In
two-sorted team semantics a team of assignments to a world variable and an individual variable
is the speaker's information state, and the uses are constancy and variation conditions on the
individual variable: constancy across the team for specific known, constancy within a world
with variation across the team for specific unknown, and variation within a world for
non-specific. The three conditions partition the teams.
Each type requires a combination of atoms, and a team meets the requirement exactly when the
type's profile lists the use the team renders. A larger team renders a use further from the
specific end, constancy passing to subteams and variation to superteams, so the use is a
monotone map from the teams to the uses ordered specific known, specific unknown, non-specific,
and a requirement is the preimage of its profile. A requirement is therefore convex, a team
between two teams meeting it meeting it too, exactly when its profile is an interval of the
uses, and only the unattested profile is not. This is the paper's account of the order of
Haspelmath's map: the profiles contiguous on the map are those with convex requirements, and of
the orderings of the three uses only the map's and its reverse make every contiguous profile
convex. Five attested types require a single atom, closed under subteams or under superteams,
and the specific unknown type the conjunction of one of each, convex and closed under neither.
German irgend-, Russian koe- and -nibud', Kannada -oo, Italian qualche- and Georgian
-γac instantiate the six attested types: the uses are the three specificity functions of
Haspelmath's map, the non-specific use being the irrealis function, and a series covers the uses
whose functions lie in the region the book draws for it.
TODO
The paper extends the system with negation and modality to derive the licensing of non-specific
indefinites and treats epistemic indefinites at length; neither is formalized here.
References