Multilinear Grammar: Ranks and Interpretations
  Multilinear Grammar provides a framework for integrating the many different syntagmatic structures of language into a coherent semiotically based Rank Interpretation Architecture, with default linear grammars at each rank. The architecture defines a Sui Generis Condition on ranks, from discourse through utterance and phrasal structures to the word, with its sub-ranks of morphology and phonology. Each rank has unique structures and its own semantic-pragmatic and prosodic-phonetic interpretation models. Default computational models for each rank are proposed, based on a Procedural Plausibility Condition: incremental processing in linear time with finite working memory. We suggest that the Rank Interpretation Architecture and its multilinear properties provide systematic design features of human languages, contrasting with unordered lists of key properties or single structural properties at one rank, such as recursion, which have previously been been put forward as language design features. The framework provides a realistic background for the gradual development of complexity in the phylogeny and ontogeny of language, and clarifies a range of challenges for the evaluation of realistic linguistic theories and applications. The empirical objective of the paper is to demonstrate unique multilinear properties at each rank and thereby motivate the Multilinear Grammar and Rank Interpretation Architecture framework as a coherent approach to capturing the complexity of human languages in the simplest possible way. 
Dafydd Gibbon and Sascha Griffiths
cs.CL