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Title:Output-Driven Maps
Authors:Bruce Tesar
Abstract:A long-standing issue of interest is the extent to which phonological maps from input (underlying) forms to output (phonetic) forms can be characterized in terms of conditions on the output forms. A traditional approach to this is found in the notion of phonological opacity (Kiparsky 1971, 1973). Here, opacity is a property of phonological processes relative to phonological maps: a process is said to be opaque if it contributes meaningfully to the analysis of a phonological map (either by applying or by not applying), but the conditions for its (non)application are not surface apparent. This makes the 'output-orientedness' of a map dependent upon the particular choice of processes used in the analysis. The dependence on processes can be particularly awkward in a theory like Optimality Theory (Prince & Smolensky 1993/2004), in which processes are not primitives of the theory, but are at best descriptive commentaries, subject to equivocation.

While the focus on phonological generalizations implicit in the process-based view is reasonable, this paper argues that there is benefit to exploring a more abstract characterization of 'output-orientedness' in phonological maps, a characterization in terms of only the maps themselves. Such a characterization is provided in this paper, in the form of the concept of output-driven map. Once the definition of output-driven map is established, it can be used to characterize different phonological maps on their own terms. It can also be used to evaluate different theoretical devices, whether process-based or not, in terms of the capacity of those devices to generate maps which are or are not output-driven.

The concept of output-driven map is dependent on a characterization of similarity between input and output forms. Intuitively, the more representational disparities there are between an input and an output, the less similar they are. A map is defined to be output-driven if, for every mapping from an input IN1 to an output OUT in the map, each input IN-X that has greater similarity to the output OUT than IN1 does also maps to output OUT. If one input maps to an output, that entails that every other input closer to the output also maps to that output. The paper includes a detailed specification of this notion under particular representational assumptions, including a fully specified definition of similarity in the relevant sense.

An analysis of Optimality Theory is then given with respect to the definition of output-driven maps. Sufficient conditions on OT systems are derived which ensure that all grammars defined by such systems generate output-driven maps. The conditions are of two types: conditions on GEN, and conditions on the constraints of CON. The conditions on constraints are of particular interest, and it is shown that from them one can derive a set of three possible constraint behaviors that can result in non-output-driven maps.

A variety of OT constraints are then examined. Several types of constraints are not capable of exhibiting any of the behaviors that can cause non-output-driven maps; this is discussed, and formal proofs are provided in the appendix. A number of constraints that have been proposed to analyze phenomena traditionally interpreted as opaque are also examined. The maps corresponding to the phenomena are shown to be non-output-driven, and in every phenomenon examined the key constraint is shown to exhibit one of the three key behaviors in causing the map to be non-output-driven. The constraint behaviors thus unify our understanding of a variety of proposals within OT for handling such phenomena, including constraint conjunction, antifaithfulness, positional faithfulness, and sympathy theory.

The proposed definition of output-driven maps captures familiar intuitions about output-orientedness in phonological maps. While still requiring representational commitments, the property of being output-driven stands apart from any particular theory relating input representations to output representations. It is likely that other properties of maps themselves wait to be discovered, perhaps defining less restrictive classes of maps, that are relevant for phonological theory. A better understanding of the properties of phonological maps, and their implications for specific theories, can only be of benefit to an evaluation of the relative strengths of competing theories.
Type:Paper/tech report
Area/Keywords:Phonology,Formal Analysis
Article:Version 1