LECTURETTE #23 OPTIMALITY One of our participants has asked me to say a little something about Optimality Theory, as it applies to syntax. Although the Optimality approach can be adapted to many, perhaps all frameworks, most of the work i know of that applies it to syntax is couched in a PPA framework (this is probably merely due to PPA's generating more research than any one of its competitors), and so i decided to discuss this subject here, in closing (for now) our perusal of PPA. Optimality Theory originated in phonology; as far as i know, the princi- pal text for that aspect of it is a 1993 book by Alan Prince and Paul Smolensky, Optimality Theory: Constraint Interaction in Generative Gram- mar (MIT Press). It has recently been adapted to syntactic research by e.g. Jane Grimshaw and Geraldine Legendre; the best publications known to me in this program are: Grimshaw, Jane. 1993. Minimal Projection, Heads, & Optimality. (Rutgers Center for Cognitive Science Technical Report 4) Piscataway, NJ: Rutgers University Center for Cognitive Science. Legendre, Geraldine, William Raymond, & Paul Smolensky. 1993. `An Optimality-Theoretic Typology of Case and Grammatical Voice Systems' BLS 19:464-478. >From my admittedly limited perspective, Optimality Theory appears to be a pretty hot ticket right now. You will recall what i have said in the past about the importance of constraints in contemporary generative theory. I've mentioned several in various lecturettes, e.g. the Case Filter, the ECP, the SPC. In *traditional* (by which, in this case, i mean roughly pre-1990) gene- rative th eory, it is typically assumed that a constraint represents a hard-and-fast rule of grammar, whether universal or gammar-particular: the presence in the grammar of a constraint against construction X means that construction X simply cannot be generated by that grammar, no way, no how. The big difference between this `traditional' assumption (and assumption was really all it was, to the best of my knowledge) and the Optimality approach is that the latter would allow for the possibility of construction X being generated -- and maybe even *used* -- under certain circumstances, in spite of the presence in the grammar of a constraint against it. How does this work? The basic idea is that in Optimality Theory con- straints don't merely exist in the grammar. They exist in relation to each other; they interact. In particular, they can be *ranked* with respect to each other. Instead of each constraint being regarded as ipso facto absolute, it is possible to say that one constraint is `weightier' than another (NB: this is my way of putting it). What this translates into is a measure of relative *cost of violation of a given constraint.* It becomes possible to say, `Construction X violates constraint C; but that's nowhere near as bad as construction Y, which violates constraint A.' If constraint A ranks higher than constraint C, meaning that the cost of violating A is greater than the cost of viola-ting C, than it is meaning- ful to say that construction X, which violates C but not A, is more gram- matical than construction Y, which violates A. Once such a hierarchical ranking of constraints has been defined, we can take an abstract, underlying form and derive from it a set of plausible superficial forms. (I'm deliberately using language suitable to Optimali- ty Theory's original use in phonological theory. Obviously, where pho- nologists talk about `forms' syntacticians are more likely to talk about `constructions' or `P-markers' or whatever.) We then evaluate these de- rived forms on the basis of whether any of them violate any constraints in the grammar and if so, which ones, and how those constraints rank with respect to each other. Obviously, derivations that violate no con- straints at all are to be preferred. But it is possible, in theory, for a well-formed underlying structure to have no superficial reflexes that enjoy this happy state. In this case, the question becomes, Which of the derived forms involves the least derivational cost? Which violates the fewest, or the least weighty, constraints? That one, once it is identi- fied, is designated by the grammar as *optimal*, to be preferred over all alternatives. For instance, in attempting to account for the requirement of Subject- Auxiliary Inversion in English interrogatives, Grimshaw posits the fol- lowing four constraints, ranked as follows: (1) Proj-P - The Projection Principle Selected complements (i.e., constituents specified in the subcat- gorization frame of, and theta-marked by, some governor) must be present in equivalent form at both DS and SS. E.g., if a verb subcategorizes for a CP complement there had better be a CP node in a complement position governed by that verb at both DS and SS. (2) Op-Spec - Operator in Specifier Position Syntactic operators (e.g., wh-elements) must be in the specifier position of some projection. (3) Ob-Hd - Obligatory Heads Heads must be filled at SS by lexical material, traces, or phi- features. (4) Min-Proj - Minimal Projection A functional projection must be functionally interpreted. I.e., a functional projection has to make a *suitable* contribution to the interpretation of the whole structure. The relevant corollary of this constraint is that individual functional projections must be *motivated*, and should not exist unless they actually contri- bute something. {In what follows, i am merely summarizing the argument presented in Grimshaw 1993, not critiquing it. I am familiar with at least one other version, in which a slightly different set of constraints, with diffe- rent ranking, is used to account for the same data. I am not here going to address the motivation or the validity of Grimshaw's list that i have just presented; all i am trying to do is convey by word and example a sense of how Optimality Theory works.} An ordinary, simple declarative clause like (5) satisfies all of these constraints (as long as it's treated as a simple IP -- the presence of a superordinate CP would violate Min-Proj), and is thus unquestionably grammatical. (5) Kim saw Hilary. Grimshaw shows that the following interrogative versions of this clause (replacing `Hilary' with a wh-element) all violate some constraint. (6) a. Kim saw whom? b. Whom Kim saw? c. Whom did Kim see? (6a) has an operator -- the wh-element -- in complement rather than spe- cifier position, thereby violating Op-Spec, a high-ranking constraint. (6b & c) both have an `unmotivated', non-contributing CP projection, thereby violating Min-Proj; but both satisfy Op-Spec by putting `whom' in the Spec of CP. Since Op-Spec outranks Min-Proj, both (6b) and (6c) are to that extent preferable to (6a). But (6b) also violates Ob-Hd by not filling the head of CP; (6c) satisfies this constraint by moving Infl to the head of CP and generating the dummy auxiliary `do' to manifest it. Thus, (6a) violates a fairly high-ranking constraint; (6c) violates a low-ranking one; (6b) violates the same constraint (6c) violates and another one as well, and is therefore more costly. (6c) is the least costly, and therefore the most grammatical of the three. Note that no single *interrogative* can be generated that satisfies all constraints. I hope this is reasonably clear. As Grimshaw says (1993:2), `The core of Optimality [Theory] is these three ideas: (7) a. Constraints can be violated b. Constraints are ranked c. The optimal form is grammatical' Obviously, as with the plain old ordinary declarative sentence in (5), it is possible within this theory to have constructions that violate no con- straints at all; but it is equally possible for it to be impossible to fulfill a certain necessary function of language without violating at least some constraint(s); the goal, in such cases, is to violate (i) as few as possible and (ii) lower-ranking constraints rather than higher- ranking ones. That's the basics of Optimality Theory in syntax. There are two more points that need to be made. One very important point is that the de- tails of the constraints, and their ranking, are *language-specific*: Some languages may have constraints that others don't have at all, and some constraints that are common to more than one language may be ranked differently vis-a-vis each other in different languages. The other is that the ranking of constraints need not be exhaustive. It is logically possible within a single grammar to have a variety of con- straints, some of which are ranked in relation to each other and others of which are not; it's even possible, at least in theory, to have to constraints that outrank all others but which are unranked with respect to each other. Most of the work i've been doing in Optimality Theory has been in exploring this possibility, and the notion that it might enable us to account in a formal theoretical framework for optionality and varia- bility in a single grammar. * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * For now, that's the end of our survey of Chomskyan theory. Soon i will start talking about Relational Grammar and Arc-Pair Grammar. Best, Steven --------------------- Dr. Steven Schaufele 712 West Washington Urbana, IL 61801 217-344-8240 fcosws@prairienet.org **** O syntagmata linguarum liberemini humanarum! *** *** Nihil vestris privari nisi obicibus potestis! ***