Abstract
Understanding a linguistic theory within OT requires an exact characterization of the ranking conditions necessitated by data. These conditions determine the formal shape of the grammar while providing the crucial link between the data and its interpretation. We introduce an algorithm (‘Fusional Reduction’, FRed) which calculates the necessary and sufficient ranking conditions inherent in any collection of candidates and presents them in a maximally concise and informative way. The algorithm, stemming from the original proposal of Brasoveanu 2003, is set within the fusional ERC theory of Prince 2002a. In this context, the Most Informative Basis and the Skeletal Basis emerge as the two important types of reduced representations of ranking structure. We examine their properties and show how FRed produces them from data. Fine-grained FRed is compared with broad-stroke RCD (Tesar and Smolensky 1993, Tesar 1995 et seq.), and RCD is reinterpreted and embraced within FRed as a simplified, information-losing sub-case. Finally, FRed is compared with other related algorithms in structure, worst-case complexity, and relevance to the analytical enterprise. This paper revises Brasoveanu and Prince 2005, 2007; Prince and Brasoveanu 2010 gives a more formal perspective, with proof of the theorems.
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ROA = Rutgers Optimality Archive. http://roa.rutgers.edu.
Anderson, Alan Ross, and Nuel D. Belnap Jr., eds. 1975. Entailment: the logic of relevance and necessity, Vol. 1. Princeton: Princeton University Press.
Baković, Eric. 2000. Harmony, dominance, and control. PhD dissertation, Rutgers University, New Brunswick. ROA-360: 25–50.
Brasoveanu, Adrian. 2003. Minimal fusion normal form. Manuscript, Rutgers University. http://people.ucsc.edu/~abrsvn/MFNF.pdf.
Brasoveanu, Adrian, and Alan Prince. 2005. Ranking and necessity, Part I (first version). ROA-794.
Brasoveanu, Adrian, and Alan Prince. 2007. Fusional reduction and the logic of ranking arguments in OT. Handout. In 31st Penn linguistics colloquium. University of Pennsylvania.
Gigerenzer, Gerd, and Daniel G. Goldstein. 1996. Reasoning the fast and frugal way: models of bounded rationality. Psychological Review 103(4): 650–669.
Gigerenzer, Gerd, Peter M. Todd, and the ABC Research Group. 1999. Simple heuristics that make us smart. New York: Oxford University Press.
Grimshaw, Jane. 1997. Projection, heads, and optimality. Linguistic Inquiry 28(4): 373–422. ROA-68.
Hammer, Peter, and Alexander Kogan. 1993. Optimal compression of propositional Horn knowledge bases: complexity and approximation. Artificial Intelligence 64: 131–145.
Hayes, Bruce. 2004. Phonological acquisition in optimality theory: the early stages. In Constraints in Phonological Acquisition, eds. René Kager, Joe Pater, and Wim Zonneveld, 158–203. Cambridge: Cambridge University Press. Also as ROA-327.
Hayes, Bruce, Bruce Tesar, and Kai Zuraw. 2004. OTSoft. http://www.linguistics.ucla.edu/people/hayes/otsoft/.
Lombardi, Linda. 1999. Positional faithfulness and voicing assimilation in optimality theory. Natural Language & Linguistic Theory 17: 267–302.
Merchant, Nazarré. 2008. Discovering underlying forms: contrast pairs and ranking. PhD dissertation, Rutgers University, New Brunswick. ROA-964.
Meyer, Robert K. 1975. Chapters 29.3 and 29.12. In Vol. 1 of Entailment: the logic of relevance and necessity, eds. Alan Ross Anderson and Nuel D. Belnap Jr. Princeton: Princeton University Press.
Parks, Zane R. 1972. A note on R-mingle and Sobociński’s three-valued logic. Notre Dame Journal of Formal Logic 13: 227–228.
Prince, Alan. 1998. A proposal for the reformation of tableaux. ROA-288.
Prince, Alan. 2000. Comparative Tableaux. ROA-376.
Prince, Alan. 2002a. Entailed ranking arguments. ROA-500.
Prince, Alan. 2002b. Arguing optimality. ROA-562.
Prince, Alan. 2006a. Lectures on optimality theory, Università degli Studi di Verona. Lecture 2.
Prince, Alan. 2006b. Implication & impossibility in grammatical systems. ROA-880.
Prince, Alan. 2006c. No more than Necessary: beyond the Four Rules, and a bug report. ROA-882.
Prince, Alan. 2008a. The proper treatment of ranking in OT. Manuscript, Rutgers University.
Prince, Alan. 2008b. ERC minimization is tractable. Manuscript, Rutgers University.
Prince, Alan. 2008c. OTWorkplace. Freeware. http://ling.rutgers.edu/people/faculty/prince.html.
Prince, Alan. 2009. RCD–the movie. ROA-1057.
Prince, Alan, and Adrian Brasoveanu. 2010. The formal structure of ranking arguments in OT. Manuscript, Rutgers University and UC Santa Cruz.
Prince, Alan, and Paul Smolensky. 2004. Optimality theory: constraint interaction in generative grammar. Oxford: Blackwell. Revised from ROA-537 (1993 version).
Prince, Alan, and Bruce Tesar. 2004. Learning phonotactic distributions. In Constraints in phonological acquisition, eds. René Kager, Joe Pater, and Wim Zonneveld, 245–291. Cambridge: Cambridge University Press. Also as ROA-353 and RUCCS-TR-54.
Prince, Alan, and Bruce Tesar. 2008. RUBOT. Freeware, Dept of Linguistics, Rutgers University.
Riggle, Jason. 2007. Efficiently Computing OT Typologies. Talk at Linguistic Society of America Annual Meeting. Anaheim, CA. Abstract available at http://clml.uchicago.edu/~max/pdf/abstract-efficiently_computing_ot_typologies.pdf.
Samek-Lodovici, Vieri. 1992. Universal constraints and morphological gemination: a crosslinguistic study. Revised as “A Unified Analysis of Cross-linguistic Morphological Gemination,” 1996: ROA-149.
Samek-Lodovici, Vieri, and Alan Prince. 1999. Optima. RuCCS-TR-57. ROA-363.
Samek-Lodovici, Vieri, and Alan Prince. 2005. Fundamental Properties of Harmonic Bounding. RUCCS-TR-71: http://ruccs.rutgers.edu/tech_rpt/harmonicbounding.pdf. Corrected 2005 as ROA-785.
Sobociński, Bolesław. 1952. Axiomatization of a partial system of three-valued calculus of propositions. The Journal of Computing Systems 1: 23–55.
Tesar, Bruce. 1995. Computational optimality theory. PhD Dissertation, University of Colorado at Boulder. ROA-90.
Tesar, Bruce. 1997a. Multi-recursive constraint demotion. ROA-197.
Tesar, Bruce. 1997b. Using the mutual inconsistency of structural descriptions to overcome ambiguity in language learning. In Proceedings of the North East Linguistic Society 28, eds. Pius N. Tamanji and Kiyomi Kusumoto, 469–483. Amherst: GLSA, University of Massachusetts.
Tesar, Bruce, and Alan Prince. 2005. Using phonotactics to learn phonological alternations. In Proceedings of the thirty-ninth conference of the Chicago Linguistics Society, Vol. II. The Panels. ROA-620.
Tesar, Bruce, and Paul Smolensky. 1993. The learnability of optimality theory: an algorithm and some basic complexity results. ROA-2.
Tesar, Bruce, and Paul Smolensky. 2000. Learnability in optimality theory. Cambridge: MIT Press. Also ROA-156.
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Brasoveanu, A., Prince, A. Ranking and necessity: the Fusional Reduction Algorithm. Nat Lang Linguist Theory 29, 3–70 (2011). https://doi.org/10.1007/s11049-010-9103-3
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DOI: https://doi.org/10.1007/s11049-010-9103-3