Multidimensional Semantics with Unidimensional Glue Logic

We present an implementation of multidimensional semantics in Glue Semantics. Our approach differs from the proposal of Arnold and Sadler (2010) by restricting multidimensionality to the meaning language and therefore avoiding the introduction of tensors in the compositional glue logic. We use a construction from category theory --- monads --- to create structured mappings from the algebra of unidimensional semantics to the multidimensional case. Monads have already been successfully employed in theoretical computer science to provide a denotational semantics of side effects. Here we follow the suggestion of Shan (2001) to use monads to model semantic phenomena and show how monads can be used to capture the analysis of natural language expressions like appositives and expressives. We argue that monads allow us to keep the simplicity of unidimensional composition while also allowing the ability to track multiple meaning dimensions and to control information flow between these different dimensions appropriately.