ABA and the combinatorics of morphological features

In several three cell paradigms, it has been observed that one logically conceivable pattern – ABA under some arrangement of cells – is unattested. Existing approaches assume that such *ABA generalizations provide evidence for feature inventories which are restricted to features that stand in containment relations, and are thus subject to P ā ṇinian rule order. We present a novel approach to *ABA generalizations that derives from general properties of feature-based morphology. To this end, we develop a formal account of the widespread view that morphological paradigms derive from rules that relate abstract features from an inventory to morphological exponents. We demonstrate that the feature-based view restricts the space of typological patterns even without any further assumptions. We show furthermore that the feature-based theory derives *ABA as a special case of a broader class of generalizations if the number of features in the inventory must be minimal, and that these generalizations arise under a variety of general assumptions about feature-algebras (extrinsically ordered or P ā ṇinian and with or without feature intersection). We discuss which explanation might be correct for actual cases of *ABA constraints, and we explore the consequences of the feature-based general approach for a range of paradigm sizes including those with more than three cells.