On the Logic of Expansion in Natural Language
Glyn V. Morrill, Oriol Valentín · Lecture notes in computer science · 2016
Abstract We consider, for intuitionistic categorial grammar, an iteration modality with a rule of Mingle and an infinitary left rule, similar to infinitary action logic. Newly, we give Curry-Howard labelling for the iteration modality, in terms of lists, and we prove soundness and completeness of displacement calculus with additives and this modality, for phase semantics. This result has as a corollary semantic Cut-elimination. We review linguistic application of the iteration modality to unbounded addicity iterated coordination, and we present an application of a calibrated version of the iteration modality to an unbounded addicity respectively construction, this being to our knowledge the first account of respectively taking care of cases $$n>2$$ n>2 .