Minimal logics for reasoning with ambiguous expressions

Author: Jaspars, Jan

Editor:

Alshawi and Crouch defined a simple multi-valued truth-conditional semantics for quasi logical form, a representation language for underspecified expressions. We incorporate this so-called monotonic semantics within the setting of plain propositional logic, and investigate the underlying calculi. It turns out that evaluation of ambiguous expressions with respect to a partial disambiguation, that is, possible readings maybe excluded on the moment of interpretation, yields the most attractive notion of validity in this setting. Besides the fact that it satisfies characteristic criteria of 'ambiguous reasoning', the underlying logic is also a suitable candidate as a minimal calculus for this task. Natural extensions of the calculus correspond to intuitive constraints on partial disambiguations. The paper presents this calculus and different extensions in a special Gentzen format, well-equipped for reasoning with 'multiple readings'. Two technical appendices contain the completeness proofs for the various calculi.