Sets, rules and natural classes: [ ] vs. { }




phonology, features, set theory, logic, unification, phonological rules


We discuss a set-theoretic treatment of segments as sets of valued features and of natural classes as intensionally defined sets of sets of valued features. In this system, the empty set { } corresponds to a completely underspecified segment, and the natural class [ ] corresponds to the set of all segments, making a feature ± Segment unnecessary. We use unification, a partial operation on sets, to implement feature-filling processes, and we combine unification with set subtraction to implement feature-changing processes. We show how unification creates the illusion of targeting only underspecified segments, and we explore the possibility that only unification rules whose structural changes involve a single feature are UG-compatible. We show that no such Singleton Set Restriction can work with rules based on set subtraction. The system is illustrated using toy vowel harmony systems and a treatment of compensatory lengthening as total assimilation.


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Bale, A., Papillon, A., & Reiss, Ch. (2014). Targeting underspecified segments: A formal analysis of feature changing and feature filling rules. Lingua, 148, 240-253.

Bale, A., & Reiss, Ch. (2018). Phonology: A Formal Introduction. Cambridge, MA: MIT Press.

Bendjaballah, S., & Haiden, M. (2008). A typology of emptiness in templates. In J. Hartmann, V. Hegedus, & H. van Riemsdijk (Eds.) Sounds of Silence: Empty Elements in Syntax and Phonology (pp. 23-59). Amsterdam: Elsevier.

Borrelli, D. A. (2013). Raddoppiamento Sintattico in Italian. A Synchronic and Diachronic Cross-dialectical Study. New York: Routledge.

Chomsky, N. (2000). Language as a natural object. In New Horizons in the Study of Language and Mind (pp. 106-133). Cambridge: Cambridge University Press.

Chomsky, N., & Halle, M. (1968). The Sound Pattern of English. New York: Harper & Row.

Côté, M.-H. (2008). Empty elements in schwa, liaison and h-aspiré: The French Holy Trinity revisited. In J. Hartmann, V. Hegedus, & H. van Riemsdijk (Eds.) Empty Elements in Syntax and Phonology (pp. 61- 103). Amsterdam: Elsevier.

Dell, F., & Elmedlaoui, M. (1985). Syllabic consonants and syllabification in imdlawn tashlhiyt berber. Journal of African Languages and Linguistics, 7, 105-130.

Flemming, E. (2005). Deriving natural classes in phonology. Lingua, 115, 287-309. DOI:

Halle, M. (1964). On the bases of phonology. In J. J. Katz, & J. Fodor (Eds.) The Structure of Language (ch. 9, pp. 324-333). Englewood Cliffs, NJ: Prentice-Hall.

Hayes, B., & White, J. (2015). Saltation and the p-map. Phonology, 32, 267-302.

Hyman, L. (1985). A Theory of Phonological Weight. Dordrecht: Foris.

Inkelas, Sh. (1995). The consequences of optimization for underspecification. In J. Beckman (Ed.), Proceedings of the North East Linguistic Society, 25 (pp. 287-302). Philadelphia, PA: University of Pennsylvania Graduate Linguistic Student Association.

McCarthy, J. (1988). Feature geometry and dependency: a review. Phonetica, 45, 84-108.

Mielke, J. (2008). The Emergence of Distinctive Features. Oxford: Oxford University Press.

Peterson, G. E., & Harary, F. (1961). Foundations of phonemic theory. In R. Jakobson (Ed.) Structure of Language and Its Mathematical Aspects. Proceedings of Symposia in Applied Mathematics, 12 (pp. 139-165). Rhode Island: American Mathematical Society.

Reiss, Ch. (1995). A Theory of Assimilation, with Special Reference to Old Icelandic Phonology. Doctoral Dissertation, Harvard University, Department of Linguistics.

Reiss, Ch. (1996). Deriving an implicational universal in a constrained OT grammar. In K. Kusumoto (Ed.), Proceedings of North East Linguistic Society, 27 (pp. 303-318). Cambridge, MA: Harvard University & MIT Graduate Linguistic Student Association.

Reiss, Ch. (2003). Quantification in structural descriptions: Attested and unattested patterns. The Linguistic Review, 20, 305-338.

Reiss, Ch. (2019). Are Saltations Real? Ms. Concordia University.

Sagey, E. C. (1986). The Representation of Features and Relations in Nonlinear Phonology. Doctoral Dissertation, Massachusetts Institute of Technology, Cambridge, MA.

Shen, D. T.-Ch. (2016). Precedence and Search: Primitive Concepts in Morpho-phonology. Doctoral Dissertation, National Taiwan Normal University, Taipei.

Trommer, J. (2015). Moraic affixes and morphological colors in Dinka. Linguistic Inquiry, 46, 77-112.



How to Cite

Bale, A. ., Reiss, C. ., & Ta-Chun Shen, D. . (2019). Sets, rules and natural classes: [ ] vs. { }. Loquens, 6(2), e065.




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