Optimality Theory and the Problem of Constraint Aggregation

1. The Issue Of recent changes in linguistic theory, the shift from derivations to constraints is among the most substantive. Central to this is Optimality Theory (OT; Prince & Smolenksy 1993), which – unlike, e.g., Chomsky & Lasnik’s Filters or Pān. ini’s As.t.ādhyāȳı – claims that structural well-formedness (grammaticality) is enforced by sharply conflicting, mutually incompatible constraints. As it is impossible to satisfy all constraints simultaneously, grammars must resolve conflicts to determine an input’s ‘surface representation’, the form ‘most harmonic’ with the constraints. Prince & Smolensky, and most subsequent work, resolve conflicts by ‘rank[ing] constraints in a strict dominance hierarchy ’. We question this position and develop a formal mathematical approach to constraint-conflict resolution. This facilitates a recharacterisation of OT’s difficulties into problems for constraint-based grammar per se versus problems that are artefacts of conflict-resolution via strict dominance hierarchies. The formalism also shows that OT occupies a well-defined position in the space of logically possible constraint-based grammars and that modifications to OT (e.g., Sympathy Theory (McCarthy 1998); Boolean operations on constraints (Crowhurst & Hewitt 1999)) diverge from OT uniformly, on one formal ‘dimension’. So, we may classify these modifications according to how greatly they increase the power of the theory. Further, we can determine what phenomena fall fully beyond the logical remit of constraint-based theories, and can provide a condition that a theory must satisfy in order to count as being constraint-based. This establishes two falsifiability criteria for Prince & Smolensky’s claim that ‘Universal Grammar consists largely of a set of constraints on representational wellformedness’ and that grammaticality is a matter of structural well-formedness.