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Boolean operations and constraint interaction in Optimality Theory

This paper develops a theory of constraint interactions in which the requirements of two or more individual constraints are co-ordinated as a unit, or macro-constraint. Macro-constraints are required to account for certain types of phonological dependency; specifically, cases in which a complex linguistic pattern is co-conditioned by multiple factors. We examine examples of such patterns in Diyari, Zezuru Shona, Dongolese Nubian, and Bolivian Guaraní and show that an analysis which appeals to macro-constraints predicts attested outputs under otherwise standard assumptions concerning the evaluation of interacting constraints in OT. The behaviour of macroconstraints in restricting phonological behaviour reveals intriguing parallels with operations of conjunction, disjunction, and implication familiar from classical (or Boolean) logic. The analogy with logic is developed extensively, focussing on the operation of conjunction, and on differences between conjunction and implication. Finally, we show that the behaviours of constraints interacting under co-ordination bring into sharper focus subtle EVAL effects which do not emerge * This paper has profitted from the input of a number of colleagues. We thank John Alderete, Laura Benua, Luigi Burzio, Steven Crain, Chip Gerfen, Kleanthes Grohmann, John McCarthy, Tivoli Majors, Alan Prince, Doug Pulleyblank, Paul Smolensky, and Bill Turkel, all of whom made useful comments and contributions at some point, or who discussed the ideas in this paper with one of the authors. We are especially grateful to Laura Downing and Scott Myers for extensive written comments on an earlier version, and for lively discussion. Peter Austin generously corresponded with us concerning the Diyari data. The Bolivian Guaraní data were elicited by Crowhurst in 1996 in Camiri, Bolivia from Bismarck Abayo, Vicenta Camargo, Silvia Chumira, and Floi, native speakers of this language. Crowhurst's fieldwork was funded by a ILAS travel grant and a University Research Council grant, both from the University of North Carolina. Versions of this work have been presented to audiences at NELS, the University of British Columbia, the University of Arizona, and the University of Maryland. Hewitt acknowledges support for this work from SSHRCC grant # 410-92-1629 to Patricia A. Shaw. Comments should be directed to both authors at mjcrowhu@gibbs.oit.unc.edu and mhewitt@din.cc.brandeis.edu.