| Description |
Idempotency requires any phonotactically licit forms to be faithfully realized. Idempotency is relevant for phonological theory, as its failure characterizes a class of opaque phonological patterns known as chain shifts. Idempotency is also relevant for learnability, as it ensures the computational soundness of the learner\'s assumption of faithful underlying representations. This paper derives tight conditions on the faithfulness constraints for idempotency in constraint-based phonology and develops an intuitive interpretation of these conditions. The intuition is that faithfulness constraints measure the phonological distance between underlying and surface 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. These equivalences hold under various assumptions, crucially including McCarthy\'s (2003) generalization that (faithfulness) constraints are all categorical.
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