The logic of ambiguity
The paper proposes a logic of ambiguity that takes a large
number of natural intuitions about ambiguous entailment
into account, by employing evaluation in models with a
disambiguation function. Also, the logic satisfies a
natural requirement of monotonicity: ambiguous entailments
are preserved under further disambiguation. The
entailment notion is axiomatized using Gentzen sequents,
and the axiomatization is shown to be complete. Next, it
is indicated how the logic can be extended in a natural
way with a well behaved implication operator. Finally we
discuss further extensions to make our treatment of
ambiguity suitable for the expressive formalisms used in
natural language semantics.
Jan van Eijck and Jan Jaspars