Consequences of Candidate Omission

1 Introduction

In this squib, we explore the generative consequences of candidate omission for constraint-based grammars. In principle, the candidate set for an input form i is the range of Gen(i) for a given generating function Gen (see Prince and Smolensky 1993:17). In practice, however, analyses often cover just a few candidates that are deemed relevant. The consequences of this practice are the focus of this squib.

Whether the omission is by oversight or by principle, a range of defects can readily arise because there are situations where, even though an analysis might include the observed/intended optimum along with a range of viable competitors, it is still possible to draw erroneous inferences about languages and typologies owing to the omission of a single candidate.

Aside from the—unfortunately familiar—problem of discovering an omitted competitor that breaks one’s current analysis because it is more harmonic than the intended/observed form, there are three other risks associated with candidate omission that we discuss here:

1. 1. Omission of certain candidates—even suboptimal ones—can lead to flawed generalizations about how observed patterns extend to novel forms.

2. 2. This can occur even for intentional “principled” omission if it is derived post hoc, rather than via the generative mechanism of the grammar.

3. 3. These errors can multiply explosively when generating typologies.

For the sake of simplicity, the examples and discussion (up until section 5) are couched in terms of the ranked constraint interactions of Optimality Theory (OT; Prince and Smolensky 1993, McCarthy and Prince 1995, Kager 1999). However, our conclusions are equally applicable to grammars with weighted constraints such as those in Goldsmith 1989, 1993, 1994, Goldsmith and Larson 1990, Legendre, Miyata, and Smolensky 1990, Bosch 1991, Wiltshire 1992, Legendre, Sorace, and Smolensky 2006, Pater 2009, and Potts et al. 2009.

2 Candidate Omission

In this section, we illustrate a range of ways in which the omission of candidates can corrupt an analysis. The basic problem can be illustrated with an extremely simple pair of schematic examples, shown in (1) and (2).

1. 1.

In this schematic example, each constraint ranking produces a distinct outcome (i.e., candidates a and c are optimal if C1 ≫ C2 but b and d are optimal if C2 ≫ C1). Consider, however, the consequences of omitting one of the candidates, as in (2).

1. 2.

With the omission of candidate d, T₁ and T₂′ still allow two distinct outcomes, but now the ranking C2 ≫ C1 selects candidates b and c (instead of b and d).

We will refer to each of these outcomes as a language. Specifically, we say that language L = {(T₁, a), (T₂′, c)} is generated by ranking R = C1 ≫ C2 over tableaux {T₁, T₂′} if R makes a and c optimal in their respective tableaux. We assume each T_n contains the candidate set for one input form. Ideally, this set should be the complete output of Gen, but this definition also covers languages implied by candidate sets that fall short of the ideal. We will say that a given candidate has been omitted from an analysis if (a) its absence has not been motivated by Gen or an undominated constraint and (b) there is some ranking/weighting under which it would have been optimal.

There are three general cases where omitting a candidate like d in example (1) can be problematic. The first—and somewhat trivial—case arises when a form like d is among those that the analyst intends the grammar to generate. This error can be readily avoided if a tableau is created for each intended optimum.

The second case arises when the analyst intends the grammar to generate a form like c. In this case, omitting d leads to the conclusion that c is generated by a stratified hierarchy with C1 and C2 in the same stratum despite the fact that C1 must dominate C2 to rule out d. In this case, we say that the analysis is incomplete.

The third—and most pernicious—case arises when the analyst intends the grammar to generate a pair of forms...