Idempotency, Output-Drivenness and the Faithfulness Triangle Inequality: Some Consequences of McCarthy’s (2003) Categoricity Generalization

Abstract

Idempotency requires any phonotactically licit forms to be faithfully realized. Output-drivenness requires any discrepancies between underlying and output forms to be driven exclusively by phonotactics. These formal notions are relevant for phonological theory (they capture counter-feeding and counter-bleeding opacity) and play a crucial role in learnability. Tesar (Output-driven phonology: theory and learning. Cambridge studies in linguistics, 2013) and Magri (J of Linguistics, 2017) provide tight guarantees for OT output-drivenness and idempotency through conditions on the faithfulness constraints. This paper derives analogous faithfulness conditions for HG idempotency and output-drivenness and develops an intuitive interpretation of the various OT and HG faithfulness conditions thus obtained. The intuition is that faithfulness constraints measure the phonological distance between underlying and output forms. They should thus comply with a crucial axiom of the definition of distance, namely that any side of a triangle is shorter than the sum of the other two sides. This intuition leads to a faithfulness triangle inequality which is shown to be equivalent to the faithfulness conditions for idempotency and output-drivenness. These equivalences hold under various assumptions, crucially including McCarthy’s (Phonology 20(1):75–138, 2003b) generalization that (faithfulness) constraints are all categorical.