On Logical Operators in Natural Language. 

Roni Katzir

Natural language allows us to describe, understand, and reason about
novel situations of arbitrary complexity. However, natural language is
also riddled with a variety of apparent imperfections -- vagueness,
imprecision, arbitrariness, and context dependence, to name a few --
that seem to make it unsuitable for systematic semantic
analysis. Starting with Richard Montague (but relying on work that
goes back at least to Frege), natural language semanticists have
attempted to bring order into this apparent mess by considering
semantic interpretation together with an independently needed
syntactic system. When syntax is taken into account, and when
(following Grice) the evaluation is done in the context of
conversational reasoning, a systematic and orderly semantic system
emerges.

My focus will be certain words in natural language -- connectives,
quantifiers, and modal operators -- that are notorious for their ill
behavior in comparison with their counterparts from formal logic. I
will try to show why linguists think that such words in natural
language are actually quite well behaved and how a constrained
contribution of context (mainly in disambiguating between different
parses and in limiting the alternatives that enter an exhaustivity
computation) gives rise to the appearance of unruliness.