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

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. Tesar (2013) and Magri (to appear) 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 (2003b) generalization that (faithfulness) constraints are all categorical. The research reported in this paper has been supported by a Marie Curie Intra European Fellowship (Grant agreement number: PIEF-GA-2011-301938) and by an MIT-France seed grant. Parts of this paper have been presented at OCP 12; at WCCFL 33; at the EPG (Experimental Phonology Group) meeting at Utrecht University in June 2015; at the LSA Workshop on Computational Phonology and Morphology at the University of Chicago in July 2015; at the Rutgers Optimality Research Group in September 2015; at MIT in April 2016. Feedback from those audiences is gratefully acknowledged. Finally, I would like to thank Bruce Tesar for very useful comments on earlier versions of this paper. G. Magri SFL UMR 7023 (CNRS, University of Paris 8) 61 Rue Pouchet, 75017 Paris, France E-mail: [email protected]