Eval

The other main component of OT is the function known as Eval (for evaluator). Eval takes as its input the (large) candidate set produced by Gen and determines which candidate is the optimal one. The basic architecture of OT is diagrammed as follows: (28) OT’s basic architecture

/Input/ → Gen → {cand1,cand2, …candn} → Eval → [output]

Eval is composed of the universal constraint set (known as CON) organised in a language-specific hierarchy. The optimal candidate is the one that best satisfies the set of constraints; that is, the one which incurs the fewest violations. Constraint ranking plays a crucial role in the evaluation process, and this ranking is rigorously adhered to when candidates are compared. Because OT constraints are violable, it can be the case that the actual output (i.e. the optimal candidate) may fare worse than an ousted candidate on one or more constraints ranked beneath the determining constraint. For instance, if constrain C1 outranks C2 and C3, then the optimal candidate may fare worse

than its rival on C2 and C3, provided that it fares better on C1. As Prince and Smolensky

(1993) analogise, “azzzzz” alphabetically precedes “baaaaa”, since when it comes to alphabetical order it is the leftmost letter that is decisive irrespective of the observation that the letters farther to the right may appear to strongly support an alternative order (see also McCarthy 2002: 4).

Note that the dominance relation between constraints is transitive. This means that if C1 outranks C2 and C2 outranks C3, then C1 must outrank C3. This can be written

49

(29) Transitivity of constraint dominance: If C1» C2 and C2 » C3 then C1 » C3

Note also that in addition to being transitive, the dominance relation between constraints is strict. This is to say that it is not possible to make up for violation of higher-ranked constraints through respecting lower-ranked constraints. As Kager (1999) phrases it, “[O]ptimality does not involve any kind of compromise between constraints of different ranks” (p. 22). Tableau (30) gives a clearer picture of what we mean by strict dominance.

(30)

Candidate (30a) incurs more violations of C2,unlike (30b) which respects C2 but at the

costly expense of violating higher-ranked C1. Any candidate that violates a high-

ranked constraint that is respected by another candidate is ruled out outright, irrespective of its satisfying any lower-ranked constraints.

Strictness of dominance can also refer to the fact that “constraint violations are never added for different constraints” (Kager 1999: 23). Violating two (or more) lower- ranked constraints (C2,C3, etc.) cannot nullify a solitary violation of a higher-ranked

constraint (C1), as can be seen in tableau (31).

(31)

This clearly shows that lower-ranked constraints can in no way band together against a constraint occupying a higher hierarchical position.

C1 C2 a.  candidate a ** b. candidate b *! C1 C2 C3 a.  candidate a * * b. candidate b *!

50

It can also be the case that several candidates incur an equal number of violations of C1. In this case, all the offending candidates are handed on to be evaluated

by a lower-ranked constraint, C2. In such a situation there is said to be a “tie” between

candidates; this tie is portrayed by tableau (32), and the tie on C1 is decided by the violation of C2.

(32)

The amount of violation is also relevant to determining the actual output form; constraint violations should be kept to a minimum. In other words, a candidate that gets, say, one violation mark from C1 is better than a candidate that gets two (or more)

violation marks from this constraint. This points to an important property of OT, called ‘Economy’ by Prince and Smolensky (1993: 27).

(33) Economy Property of Optimality Theory

Banned options are available only to avoid violations of higher-ranked constraints and can only be used minimally.

Minimality of violation is illustrated by tableau (34). (34)

As well as applying to higher-ranked constraints, minimality of violation also applies to lower-ranked constraints. This means that higher-ranked constraints do not deactivate or switch off their lower-ranked counterparts, but less priority is given to violation of these latter constraints. Tableau (35) gives a picture of what we mean by minimal violation of lower-ranked constraints (Kager 1999: 24).

C1 C2 a.  candidate a * b. candidate b * *! C1 C2 a.  candidate a * * b. candidate b **!

51 (35)

C2 islower than C1, but it is still decisive as it is higher than C3.

The evaluation process is illustrated by means of a grid known as a ‘tableau’. The input is placed in the top row of the tableau, followed by the constrains‒ with the highest constrain(s) occupying the leftmost position; the importance of the constraint diminishes as the constraint moves down to the right-hand side. Constraints of different ranks are separated by solid lines, while dotted lines are used to separate equally-ranked constraints. The candidates are placed in the leftmost column, in cells just under the cell of the input: one of these candidates is selected as the actual output form, indicated by a pointing finger. An asterisk is conventionally used to indicate a violation of some constraint (the more the violations, the more the asterisks); fatal violation is indicated by means of an exclamation mark.

It should be taken into account that the optimal candidate is not necessarily flawless. It is simply selected as the most harmonic with respect to other competing candidates. The candidate chosen as the actual output form can in principle violate low- ranking constraints or even high-ranking ones as long as it fares better than its rivals. There is no way for a candidate to satisfy all constraints, as the different constraints make different requirements. This means that it is not possible to rule out all candidates in a given set.

C1 C2 C3

a.  candidate a * *

b. candidate b **!

52