A Note on Phonological Similarity in Tesar’s (2013) Theory of Output-drivenness

Tesar’s (2014) notion of output-drivenness is an attempt at characterizing nonopaque phonological mappings in terms of a notion of phonological similarity between underlying and surface levels. Tesar defines phonological similarity concretely in terms of segment strings and correspondence relations. Magri (2017) instead defines similarity axiomatically through an inequality on faithfulness constraint violations. This paper studies the formal properties of the latter axiomatic notion of similarity. In particular, it shows that Tesar’s concrete definition of similarity satisfies Magri’s axiomatization in terms of faithfulness constraints. The theory of output-drivenness reconstructed in Magri (2017) thus subsumes Tesar’s (2014) original theory as a special case. Tesar’s (2014) output-drivenness is a formal condition on phonological grammars, construed as mappings from underlying to surface (or output) forms. It demands that a grammar which maps an underlying form UR1 to some surface form SR also maps to that surface form SR any other underlying form UR2 such that UR2 is more similar to SR than UR1 is. The notion of output-drivenness is relevant to phonological theory, because non-output-drivenness formally unifies various opaque phonological phenomena. Furthermore, Tesar shows that output-drivenness has learnability implications in the context of the classical inconsistency detection approach (Merchant 2008) to the problem of learning a lexicon of underlying forms from a paradigm of surface forms. The notion of output-drivenness is predicated on a notion of phonological similarity: we need a way to compare a mapping (UR1, SR) to another mapping (UR2, SR) to establish that the underlying and surface forms in the latter mapping are more similar to each other than the underlying and surface forms in the former mapping. Tesar proposes a notion of phonological similarity concretely defined in terms of disparities between strings of segments and the correspondence relations (in the sense of McCarthy and Prince 1995) that hold among those segments. Being concretely defined in terms of the basic building blocks of phonological representations, Tesar’s notion of similarity has the advantage of being framework-independent. The corresponding notion of output-drivenness thus bridges frameworks as different as rule-based and constraint-based phonology. This is important because the phonological relevance of (non)-output-drivenness lies in its ability to characterize opaque processes extensionally (namely, at the framework-independent level of mappings from underlying to surface forms) rather than intensionally (namely, in terms of framework-dependent notions such as counter-feeding and counter-bleeding rule orderings). In Magri (2017), I explore an alternative approach whereby phonological similarity is defined not at the level of strings and correspondence relations but through an axiom on faithfulness constraint violations. Despite its reliance on faithfulness constraints, I submit that my alternative approach is not inconsistent with the desired framework-independency of output-drivenness. To start, the technical notion of disparity that Tesar relies on for its definition of similarity is really just a different name for a faithfulness constraint violation. Furthermore, Tesar does not shy away from correspondence relations despite the fact that they are a representational device needed Date: December 19, 2017. This paper has benefitted greatly from discussion with Bruce Tesar. The material in section A.5 has been conceived jointly in a dark night at Rutgers University. The research reported in this paper has been funded in part by a grant from the Agence Nationale de la Recherche (grant number ANR-16-CE38-0004-01).