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This paper investigates the interpretation of Japanese -toka and -tari, two nonexhaustive particles that receive conjunctive interpretations in upward-entailing environments, but disjunctive interpretations in downward-entailing and question contexts.
We analyze -toka and -tari as items that introduce unstructured sets of alternatives in a Hamblin-style alternative semantics (Hamblin, 1973; Kratzer and Shimoyama, 2002), and derive their conjunctive and disjunctive readings via an interaction between these sets and the semantics of the environment containing them.