  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.
