Abstract
We investigate two formalizations of Optimality Theory, a successful paradigm in linguistics.We first give an order-theoretic counterpart for the data and processinvolved in candidate evaluation.Basically, we represent each constraint as a function that assigns every candidate a degree of violation.As for the second formalization, we define (after Samek-Lodovici and Prince) constraints as operations that select the best candidates out of a set of candidates.We prove that these two formalizations are equivalent (accordingly, there is no loss of generality with using violation marks and dispensing with them is only apparent).
Importantly, we show that the second formalization is equivalent with a class of operations over sets of formulas in a given logical language.As a result, we prove that Optimality Theory can be characterized by certain cumulative logics.So, applying Optimality Theory is shown to be reasoning by the rules of cumulative logics.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Besnard, Ph. and Schaub, T., 2000, “What is a (non-constructive) non-monotone logical system?,” Theoretical Computer Science 238, 489–494.
Besnard, Ph., Mercer, R.E., and Schaub T., 2000, Optimality Theory via Default Logic, unpublished.
Frank, R. and Satta, G., 1998, “Optimality theory and the generative complexity of constraint violability,” Computational Linguistics 24, 307–315.
Ginsberg, M.L., 1994, “AI and nonmonotonic reasoning,” pp. 1–33 in Handbook of Logic in Arti-ficial Intelligence and Logic Programming, Vol. 3: Nonmonotonic Reasoning and Uncertainty Reasoning, D.M. Gabbay, C.J. Hogger, and J.A. Robinson, eds., Oxford: Oxford University Press.
Hammond, M., 2000, The Logic of Optimality Theory, ROA (390), http://roa.rutgers.edu
Kager, R., 1999, Optimality Theory, Cambridge Textbooks in Linguistics, Cambridge: Cambridge University Press.
Makinson, D., 1994, “General patterns in non-monotonic reasoning,” pp. 35–110 in Handbook of Logic in Artificial Intelligence and Logic Programming, Vol. 3: Nonmonotonic Reasoning and Uncertainty Reasoning, D.M. Gabbay, C.J. Hogger, and J.A. Robinson, eds., Oxford: Oxford University Press.
Prince, A., 2001, Entailed Ranking Arguments, ROA (500), http://roa.rutgers.edu
Prince, A. and Smolensky, P., 1993, “Optimality theory: Constraint interaction in generative grammars,” Technical Report, Rutgers University, New Brunswick (NJ), and Computer Science Department, University of Colorado, Boulder.
Samek-Lodovici, V. and Prince, A., 1999, Optima, ROA (363), http://roa.rutgers.edu
Tesar, B. and Smolensky, P., 1998, “Learnability in optimality theory,” Linguistic Inquiry 29, 229–268.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Besnard, P., Fanselow, G. & Schaub, T. Optimality Theory as a Family of Cumulative Logics. Journal of Logic, Language and Information 12, 153–182 (2003). https://doi.org/10.1023/A:1022362118915
Issue Date:
DOI: https://doi.org/10.1023/A:1022362118915