Non‐Computable Functions in Optimality Theory

Abstract

Is Optimality Theory a constraining theory? A formal analysis shows that it is, if two auxiliary assumptions are made: (1) that only markedness and faithfulness constraints are allowed, and (2) that input and output representations are made from the same elements. Such OT grammars turn out to be incapable of computing circular or infinite chain shifts. These theoretical predictions are borne out by a wide range of natural phonological processes including augmentation, alternations with zero, metathesis, and exchange rules. The results confirm, extend, and account for the observations of Anderson & Browne (1973) on exchange rules in phonology and morphology.

Using learnability as a filter on factorial typology: A new approach to Anderson and Browne's generalization

“…This generalization, stated originally in (Anderson and Browne, 1973) for exchange rules, and extended to circular chain shifts in (Moreton, 2004), raises the fascinating question, why are circular chain shifts always morphological in nature?…”

“…To understand the problem posed by exchange rules, it is necessary to review the results of some prior work, beginning with the formal analysis of circular chain shifts in (Moreton, 2004). This work showed that in a version of Optimality Theory characterized by the assumptions below, certain collections of mappings are not computable.…”

“…Thus, if sentence-level phonology exhibits evidence for an across-the-board mutation, then learners could activate IO-antifaithfulness at this level, with the emergence of otherwise unattested phonological mappings. While space limitations do not allow a complete analysis, the separation of the evidence for the lexicon and evidence for a ranking appears to provide a fresh look at a classic problem in Chinese phonology, namely the circular chain-shifting phonology of Taiwanese ((Cheng, 1968), (Chen, 2000), (Moreton, 2004)). …”

“…The undominated constraints in these systems (positional faithfulness and certain markedness constraints) again set IO-and OO-antifaithfulness in direct competition in accounting for this data, requiring BCD to decide in favor of the morphological analysis. In sum, unfaithful mappings that cannot be motivated by markedness must be accounted for with antifaithfulness, capturing Moreton's (2004) original insight into this type of problem. Repetitive , BCD has a bias against ranking constraints that refer to inputs, and this bias always favors the morphological analysis.…”

“…This approach is applied to a now classic problem, namely the finding that exchange rules are always morphological in nature ( (Anderson and Browne, 1973), (Anderson, 1992), (Moreton, 2004), cf. (Chomsky and Halle, 1968)).…”