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Model theory and the content of OT constraints
, 2002
"... We develop an extensible description logic for stating the content of optimalitytheoretic constraints in phonology, and specify a class of structures for interpreting it. The aim is a transparent formalisation of OT. We show how to state a wide range of constraints, including markedness, input–outpu ..."
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Cited by 19 (3 self)
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We develop an extensible description logic for stating the content of optimalitytheoretic constraints in phonology, and specify a class of structures for interpreting it. The aim is a transparent formalisation of OT. We show how to state a wide range of constraints, including markedness, input–output faithfulness and base–reduplicant faithfulness. However, output–output correspondence and ‘intercandidate’ sympathy are revealed to be problematic: it is unclear that any reasonable class of structures can reconstruct their proponents’ intentions. But our contribution is positive. Proponents of both output–output correspondence and sympathy have offered alternatives that fit into the general OT picture. We show how to state these in a reasonable extension of our formalism. The problematic constraint types were developed to deal with opaque phenomena. We hope to shed new light on the debate about how to handle opacity, by subjecting some common responses to it within OT to critical investigation.
Just How Many Languages Are There?
"... Optimality Theory assumes the candidate set generated for any given input is of infinite cardinality. If all of the candidates in the candidate set were potential winners (optimal candidates under some ranking), then OT would have predicted an infinite typology— there would be infinitely many possib ..."
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Cited by 1 (1 self)
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Optimality Theory assumes the candidate set generated for any given input is of infinite cardinality. If all of the candidates in the candidate set were potential winners (optimal candidates under some ranking), then OT would have predicted an infinite typology— there would be infinitely many possible languages. However, SamekLodovici and Prince (1999) have shown that in standard OT (with only markedness and IO Correspondence constraints), only a finite number of candidates from the infinite candidate set, can actually be winners—the (infinite) majority of the candidates in the candidate set is harmonically bounded, and will therefore never be selected as winners under any ranking. Their argument for the finite cardinality of the set of potential winners rests on the assumption that cardinality of CON is finite. If every possible ranking between the n constraints in CON were to select a unique winner, then there can be maximally n! different winners for any given input. The addition of nonIO Correspondence constraints to CON threatens this general result. Both OO Correspondence constraints and Sympathy constraints can result in an
Sympathy Theory and the Set of Possible Winners
, 2002
"... In a recent paper SamekLodovici and Prince (1999) show: (i) that all the potential winners (harmonically unbounded candidates) can be determined in a ranking independent way, and (ii) that this set of potential winners is finite in number. However, they did not consider the influence of sympathetic ..."
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In a recent paper SamekLodovici and Prince (1999) show: (i) that all the potential winners (harmonically unbounded candidates) can be determined in a ranking independent way, and (ii) that this set of potential winners is finite in number. However, they did not consider the influence of sympathetic constraints (McCarthy, 1999, 2003) on their results. These constraints can promote perpetual losers to the set of potential winners. With sympathetic constraints, the finiteness of the set of potential winners is therefore in question. Also, the violations assigned by sympathetic constraints are indirectly ranking dependent (via the choice of the sympathetic candidate). This paper shows that: (i) the set of potential winners is still finite even in a version of OT with sympathetic constraints, and (ii) that the harmonically bounded candidates that sympathetic constraints can promote to the set of potential winners, can be determined in a ranking independent way. It follows that SamekLodovici and Prince’s results are also valid in an OT grammar with sympathy constraints. This is an important result for two reasons: (i) If for any given input the set of potential winners were to be infinite, then an infinite typology would be predicted—there will be infinitely many possible languages. However, if the set of potential winners is finite, then only a finite typology is predicted—i.e. it results in a much more restrictive theory. (ii) If the set of potential winners can only be determined in a ranking dependent manner, then the grammar of every language (a ranking of CON) has to consider the full infinite candidate set. However, if the finite set of potential winners can be determined without recourse to a specific grammar (a specific ranking of CON), then it is in principle possible to weed out the perpetual losers before the grammar of a specific language comes into play. The grammar of any given language then needs to consider only the finite set of potential winners.