Scalar Implicatures and Existential Import: Experimental Study on Quantifiers in Natural Language
Maria Spychalska

Abstract:
The thesis discusses two properties of reasoning with quantifiers in
natural language: scalar implicatures and existential import. The
notion of scalar implicature refers in this case to inferring "not
all" from both "some" and "most", or "not most" from "some";
existential import – to the question whether the universal categorial
sentence "All A’s are B" implies that there are A’s. Traditionally it
is connected with the subalternation relation in the Aristotle’s
Square of Opposition, namely with inferring "Some A’s are B" from "All
A’s are B".
  We conducted a series of reasoning experiments to check the above
properties with respect to people’s active inference-production (which
we call active logical competence) as well as their passive evaluation
of given inferences (passive logical competence). We compared
reasoning in empty and non-empty domains. Based on our results and
especially on the lack of any connection between subject’s inferences
and emptiness of domains, we explain all the observed phenomena in
terms of scalar properties of quantifiers and refuse to analyze
inferences with universal premises and particular conclusions in terms
of existential import. We propose to treat quantifiers "some" and
"most" as vague with flexible denotations.  We provide a formalization
of vagueness of quantifiers in terms of fuzzy semantics, and assume
that quantifiers have default denotations which can be extended in the
process of reasoning. The implicature "not all" is explained by the
default meaning of "most" and "some".
  To deal with the issue of interpretation of existential sentences from
fictional discourse we propose to use a dynamic modification of
possible worlds semantics.  We treat worlds as mental constructions
describing certain world states. Existential sentences presuppose a
certain world or class of worlds that set up a domain of discourse.