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<Paper uid="W98-0903">
  <Title>Three Formal Extensions to Primitive Optimality Theory</Title>
  <Section position="2" start_page="0" end_page="0" type="intro">
    <SectionTitle>
1 Introduction
</SectionTitle>
    <Paragraph position="0"> Primitive Optimality Theory (OTP) (Eisner, 1997a), and extensions to it (e.g., Albro (1998)), can be useful as a formal system in which phonological analyses can be implemented and evaluated. However, for certain types of constraints, translation into the primitives of OTP (Eisner (1997b)) can only be accomplished by adding to the grammar a number of ad hoc phonological tiers. Because these tiers serve no phonological purpose other than to allow calculation of the constraints without adding new primitives, and because the addition of phonological tiers to an OTP grammar can have a dramatic negative impact on the efficiency of OTP implementations 1, it is preferable to avoid the addition of ad hoc tiers by adding new primitives to the system.</Paragraph>
    <Paragraph position="1"> This paper looks at three types of constraints employed throughout the Optimality Theoretic literature that cannot be translated in to the 1The computation time for an Optimality Theoretic derivation within the implementation of Albro (1998) increases exponentially with the number of tiers. The same is true for the implementation described in Eisner (1997a), although a proposal is given there for a method that might improve the situation.</Paragraph>
    <Paragraph position="2"> primitives of OTP without reference to ad hoc tiers, and proposes a formalization of these constraints that is compatible with the finite state model described in Eisner (1997a) and Albro (1998). These are constraints of existential implication (that is, of faithfulness without the requirement of alignment), constraint disjunction, and local constraint conjunction.</Paragraph>
  </Section>
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