Comparative markedness JOHN J. MCCARTHY Abstract The markedness constraints of classic Optimality Theory assign violation-marks to output candidates without reference to the input or to other candidates. This article explores an alternative conception of markedness: markedness constraints compare the candidate under evaluation with another candidate, the most faithful one. Com- parative constraints distinguish two situations: the candidate under evaluation contains an instance of a marked structure that is also present in the fully faithful candidate; or it contains an instance of a marked structure that is not present in the fully faithful candidate. Empirical consequences of comparative markedness are explored, including grandfather effects, derived environment effects, non-iterating processes, and counter-feeding opacity. Comparative markedness is found to have some advantages and some disadvantages in comparison with classic OT and alternatives like local conjunction, stratal OT, sympathy, and targeted constraints. §1. Introduction Optimality Theory (Prince and Smolensky 1993) has two types of con- straints, faithfulness and markedness. Faithfulness constraints militate against input-output disparity, and markedness constraints impose restric- tions on the output without reference to the input. For example, the input- output mapping /ab/ d –ab violates the faithfulness constraint DEP (no epenthesis), and the output form –ab violates the markedness constraint NOVCDOB (for “No Voiced Obstruents”, i.e. *[−sonorant, +voice]). This article presents a different approach to markedness. The idea is that markedness constraints assign violation-marks to output candidates Theoretical Linguistics 29 (2003), 001–051 0301–4428/03/029–001 © Walter de Gruyter Brought to you by | University of California Authenticated Download Date | 11/3/14 10:04 PM 2 John J. McCarthy by comparing them to the fully faithful candidate (FFC), which is present in every candidate set. These novel markedness constraints distinguish between: -Mappings that fail to correct a marked configuration in the FFC. E.g., the map- ping /ab/ d –ab fails to correct the marked voiced obstruent in the FFC ab. That is, the NOVCDOB violation in –ab is “old” because the fully faithful candidate ab has the same violation. and -Mappings that introduce new marked configurations. E.g., the mapping /ampa/ d amba introduces a voiced obstruent that is not present in the FFC ampa. That is, the NOVCDOB violation in amba is “new” because the fully faithful candidate ampa does not have this violation. According to this hypothesis, every traditional markedness constraint M is eliminated and replaced by two freely rankable constraints, M and O M. Between them, M and M divide up all of traditional M’s violation- N O N marks. The constraint M is sensitive to violations that are old, in the sense O that they are shared with the FFC. The constraint M is sensitive to vio- N lations that are new, in the sense that they are not shared with the FFC. For example, NOVCDOB is violated by the /ab/ d –ab mapping, while O NOVCDOB is violated by the /ampa/ d amba mapping. Dividing tradi- N tional M up in this way yields some new results, as we will see below. I call this approach comparative markedness. By distinguishing between old and new markedness violations, compar- ative markedness offers a novel perspective on several famous and not-so- famous problems. In a derived environment effect (§4.2), a phonological process is observed to occur only in contexts that are not present in the FFC. In other words, only M is ranked high enough to compel unfaith- N fulness to the input; M is ranked too low to matter. In non-iterative O processes (§5.1) and counter-feeding opacity (§5.2), a process affects only those configurations that are already present in the FFC. The ranking is therefore just the opposite: M is ranked high and M is ranked low. O N The next section looks informally at yet another consequence of com- parative markedness, the analysis of grandfather effects, where a marked structure is permitted when it is old but forbidden when it is new. Later Brought to you by | University of California Authenticated Download Date | 11/3/14 10:04 PM Comparative markedness 3 sections fill in the formal details of the theory as a whole (§3) and of the analysis of grandfather effects (§4.1). In §4.3 and §5.3, comparative markedness is compared with other approaches to these phenomena, and some advantages and disadvantages are noted. §2. Grandfather Effects Suppose that typological evidence has established that Universal Gram- mar contains the classic OT markedness constraint M — for example, some languages permit only M-obeying forms, some languages have pro- cesses that actively eliminate M-violators, and so on. Now, suppose there is a language that tolerates M-violating structures inherited from the input but blocks processes from creating those same structures. This is a “grand- father effect”. (This term, suggested to me by Ellen Woolford, is based on the expression “grandfather clause”, which is a provision in a law that exempts persons who, at the time when the law was adopted, were already engaged in activities prohibited by that law.) Grandfather effects are by no means uncommon. Archangeli and Pulleyblank (1994: 293–4) and Davis (1995) call them “target conditions”, since they specifically affect the target of a phonological process. Their relevance to comparative markedness theory was discovered by Paul de Lacy, who offers the example in (1) (cf. Mascaró and Wetzels 2001). (1) Mekkan Arabic [−voice] Assimilation (Abu-Mansour 1996, Bakalla 1973) a. Voiced obstruent assimilates to following voiceless /–agsam/ –aksam ‘he swore an oath’ /mazku:r/ masku:r ‘mentioned’ b. But not vice-versa. Assimilation can’t create marked voiced obstruents /–akbar/ –akbar, *–agbar ‘older’ /matdar/ matdar, *maddar ‘shop’ c. Otherwise, voiced obstruents, even codas, are treated faithfully /–ibnu/ –ibnu ‘his son’ /–adu:z/ –adu:z ‘old’ /dabdaba/ dabdaba ‘pitter-pat (footsteps)’ Brought to you by | University of California Authenticated Download Date | 11/3/14 10:04 PM 4 John J. McCarthy Coda obstruents become voiceless before a voiceless obstruent (1a). There is no general process of coda devoicing, however, as shown by (1c). Sign- ificantly, voiceless coda obstruents do not become voiced before voiced obstruents (1b). In short, voiced obstruents present in the input are grand- fathered (e.g., dabdaba), but new voiced obstruents cannot be created by the voicing assimilation process (/–akbar/ d –akbar, *–agbar). The mark- edness constraint NOVCDOB blocks assimilation but cannot itself compel unfaithfulness. In comparative markedness theory, the original NOVCDOB constraint is replaced by NOVCDOB and NOVCDOB. NOVCDOB is violated by new N O N instances of voiced obstruents, those not present in the FFC. NOVCDOB O is violated by old instances of voiced obstruents, those already present in the FFC. For example, *–agbar violates each of these constraints once: NOVCDOB is violated by the g, whose counterpart in the FFC –akbar is N not voiced; and NOVCDOB is violated by the b, whose counterpart in the O FFC is also voiced. Assimilation is blocked, so NOVCDOB must be ranked N above the constraint responsible for assimilation, AGREE(voice),1 which is itself ranked above the faithfulness constraint IDENT(voice), as shown in (2). (The ranking arguments are surrounded by heavy lines. Here and throughout, markedness constraints that are not the focus of discussion are shown without new/old differentiation (i.e., M and M are ranked N O together).) (2) Mekkan Arabic: NOVCDOB >> AGREE(voice) >> IDENT(voice) N /–agsam/ NOVCDOB AGREE(voice) IDENT(voice) N a. ☞ –aksam * b. (FFC) –agsam *! /–akbar/ c. (FFC) ☞ –akbar * d. –agbar *! * In (2a, b), top-ranked NOVCDOB is satisfied by both candidates because N neither introduces a new voiced obstruent. This leaves the choice up to AGREE(voice), which favors the candidate with assimilation. In (2c, d), 1 For now, I assume Lombardi’s (1999: 272) definition of AGREE: “Obstruent clusters ... agree in voicing.” For discussion, see §5.1. Brought to you by | University of California Authenticated Download Date | 11/3/14 10:04 PM Comparative markedness 5 though, the assimilated candidate *–agbar has a new voiced obstruent, and its encounter with NOVCDOB is fatal. Assimilation is therefore blocked. N (Another way to satisfy AGREE(voice) is by progressive assimilation: *–akpar. I assume, as is now standard (Beckman 1998, Lombardi 1999), that the positional faithfulness constraint IDENT-ONS(voice) is ranked above AGREE.) To show that two putatively distinct OT constraints are in fact distinct, it is sufficient to show that they are crucially ranked non-adjacently in some language’s hierarchy. In Mekkan Arabic, NOVCDOB is indeed O ranked at a different place than NOVCDOB. Because some underlying N voiced obstruents make it faithfully to the surface, even in coda position, IDENT(voice) must be ranked above NOVCDOB, as shown in (3). O (3) Mekkan Arabic: IDENT(voice) >> NOVCDOB O /–ibnu/ IDENT(voice) NOVCDOB O a. ☞ –ibnu * b. –ipnu *! By transitive closure of the rankings in (2) and (3), NOVCDOB and N NOVCDOB are ranked separately in Mekkan Arabic: f NOVCDOB >> O N AGREE(voice) >> IDENT(voice) >> NOVCDOBg. With this ranking, O NOVCDOB is visibly active on candidates derived from inputs like N /–akbar/, but NOVCDOB is not visibly active on any inputs. O The key to analyzing this and other examples of grandfather effects is the ranking of the new-affecting and old-affecting versions of a mark- edness constraint. (Hereafter, I will avoid the awkward locutions “new- affecting” and “old-affecting” by saying simply “new” and “old”. When the chronologically prior definition of a markedness constraint is referred to, I will use the word “classic”, as in “classic OT”.) The new version, M, N is ranked above the markedness constraint responsible for the process that is blocked. The old version, M, is ranked below the relevant faithful- O ness constraint, so it cannot affect M-violating structures that are already present in the input/FFC. This same schematic ranking is also at work in derived environment effects (see §4.2). The opposite ranking, with M high O and M low, is attested as well (see §5). N We will return to the analysis of grandfather effects in §4.1, but first it is necessary to formalize some of the ideas that have been treated intuitively up to this point. Brought to you by | University of California Authenticated Download Date | 11/3/14 10:04 PM 6 John J. McCarthy §3. Formalization As the discussion in §2 indicated, M and M recognize, respectively, that O N a candidate retains some instance of a marked configuration and that a candidate introduces a new instance of a marked configuration, relative to the FFC. What we need, then, is a way of talking about a specific instance of a marked configuration in a candidate and a way of talking about what it means to inherit a marked configuration or to introduce a new one. An unambiguous characterization of the FFC is also required. The intuition to be captured is this: a constraint violation is new if the corresponding material in the FFC does not violate that constraint. For instance, the mapping /ampa/ d amba introduces a new NOVCDOB vio- lation relative to the FFC ampa. Differences between candidates that are not relevant to a constraint’s applicability do not make a violation new — e.g., the mapping /anba/ d amba, though unfaithful, does not introduce a new NOVCDOB violation relative to the FFC anba. Furthermore, a simple count of violation-marks is not enough to determine newness. The map- ping /ampab/ d ambap, with both post-nasal voicing and final devoicing, introduces a new NOVCDOB violation relative to the FFC ampab, even though ambap and ampab have exactly one NOVCDOB violation-mark each. To express these intuitions formally, it is necessary to define what it means to apply a markedness constraint to a form. Two notions will be essential. One is the locus of violation of a markedness constraint in a candidate. This is the spot in the candidate where the constraint is violated; for example, the locus of violation of NOVCDOB in amba is the segment b. The other notion is t-correspondence. This is a version of correspondence that has been transitivized, using the shared input to link two output candidates. Together, these elements provide a foundation for defining comparative markedness. The locus of violation of a markedness constraint M in a candidate cand is determined by the definition of M and the contents of cand.2 Every 2 I am grateful to Marc van Oostendorp for suggesting an approach along these lines. Something like this is also implicit in Crowhurst and Hewitt’s (1997) notion of the focus of a constraint. Brought to you by | University of California Authenticated Download Date | 11/3/14 10:04 PM Comparative markedness 7 markedness constraint M is defined in terms of its locus-of-violation i function Loc. Loc is a function from a candidate form to a set (strictly i i speaking, a multi-set) of loci of violation, which are segments in that candidate. (4) Loc Functions in General Loc(cand) d {locus, locus,...}, where locus is a segment in 1 2 j the candidate cand. On this view, Loc is simply the definition of M, so a Loc function is stipu- i i lated for each constraint. Some proposed Loc functions associated with familiar markedness constraints are given in (5). (5) Some Locus Functions LOC w Return every C, where C is [−sonorant, +voice]. NoVCDOB LOC w Return every V, where V is initial in some ONSET syllable. LOC w Return every C, where C is final in some syllable. NO-CODA LOC w Return every V, where V is the head of an PARSE-SYLL unfooted syllable. LOC w Return every V, where V is the head of a syllable FT-BIN that is the head of a unary foot. The definitions in (5) reflect two tentative assumptions: loci are individual segments, not strings; and constraints on structures usually return the heads of those structures as loci. This first pass through comparative markedness theory will be sufficient for this article. Some further issues should not go unremarked on, how- ever. First, because we will need to talk about corresponding loci in different candidates, loci must be elements that stand in correspondence (see (6)). Segments, at least, do correspond, but it is controversial whether features or prosodic constituents do, and relations like association lines certainly do not. Whatever the elements of correspondence turn out to be, they will also be the loci of markedness violation. Second, for contextual constraints, the choice of locus may not be obvious and it may ultimately prove necessary to allow strings of segments to be loci. Third, gradient constraints in general, and gradient alignment constraints in particular, cannot be defined in terms of a function that returns instances of a marked Brought to you by | University of California Authenticated Download Date | 11/3/14 10:04 PM 8 John J. McCarthy structure. For example, ALIGN(Ft, Word, L), as defined in McCarthy and Prince (1993), assigns for every foot one violation mark for every syl- lable standing between that foot and the left edge of the word. Elsewhere (McCarthy 2002c), I have argued that there are no gradient constraints, and so this potential impediment to redefining markedness in terms of Loc functions can be eliminated. Under this new approach to defining markedness constraints, a classic constraint M could be said to assign its violation marks in the following i way. M is defined by some locus function Loc. The result of applying M i i i to cand is a number of violation-marks equal to the cardinality of the set obtained by applying Loc to cand. The comparative markedness con- i straints M and M, which replace M, use the same function Loc. But the O i N i i i comparative constraints must additionally check whether the members of the locus set are new or old violations. Therefore, the next step in formalizing comparative markedness theory is defining what it means for two candidates from the same input to share a locus of violation. M constraints assign marks only for loci that are O shared with the FFC; M constraints assign marks only for loci that are N not shared with the FFC. This sharing relation holds between two candi- dates derived from the same input, so it must be mediated by correspon- dence. Correspondence theory (McCarthy and Prince 1995, 1999) relates inputs to outputs (though see §4.2 for extension to other correspondence relations), so a correspondence relation that is transitivized by way of the input is required. This t-correspondence relation is defined in (6). (6) T-correspondence Let cand1 and cand2 be two candidates from input inp. Let s1 be a segment (or other corresponding element) in cand1 and s2 be a seg- ment in cand2. Then s1 t-corresponds to s2 iff s1 corresponds to some segment s-inp in inp and s2 also corresponds to s-inp. We say then that s1 (cid:1) s2, with (cid:1) standing for the correspondence relation t t obtained through transitivity. In other words, the segments in different candidate forms t-correspond if they correspond to the same elements in the input. Each candidate brings with it its own correspondence relation (cid:1), so different relations are i involved in each link of the chain. With s1 (cid:1) s-inp (cid:1) s2 = s1 (cid:1) s2, we 1 2 t can sensibly compare loci of violation in different candidates. Brought to you by | University of California Authenticated Download Date | 11/3/14 10:04 PM Comparative markedness 9 We are now ready to combine these two notions, the Loc function and t-correspondence, to form a theory of comparative markedness. A com- parative constraint M is a function from the 3-tuple (cand, FFC, (cid:1)) to X t zero or more violation-marks. The old and new versions of a constraint are distinguished according to the definitions in (7). (7) Comparative Markedness Defined M(cand, FFC, (cid:1)) w Let Loc(cand) = {c, c, c,...} and let N i t i 1 2 3 Loc(FFC)={f, f, f, ...}. For each c i 1 2 3 m that lacks a t-correspondent among f , n assign one violation mark. M(cand, FFC, (cid:1)) w Let Loc(cand) = {c, c, c,...} and let O i t i 1 2 3 Loc(FFC)={f, f, f, ...}. For each c i 1 2 3 m that has a t-correspondent among f , n assign one violation mark. For example, *–agbar in (2d) contains two loci of NOVCDOB violation. One of those loci is g. It is a voiced obstruent, but it does not t-correspond to a voiced obstruent in the FFC –akbar. By virtue of this g, then, *–agbar receives one violation-mark from NOVCDOB. The other locus of violation N is b. It too is a voiced obstruent, and moreover it t-corresponds to a voiced obstruent in the FFC. By virtue of this b, *–agbar receives a violation- mark from NOVCDOB as well. On the other hand, –akbar in (2c) violates O only NOVCDOB. Since –akbar is itself the FFC, all of its markedness O violations are perforce shared with the FFC, and so it can only violate old markedness constraints. To sum up, M and M keep track of new and old markedness viola- N O tions in a candidate. A markedness violation is new if the corresponding segment in the FFC is not similarly marked; a markedness violation is old if the corresponding segment in the FFC is similarly marked.3 This leaves one last foundational matter to be dealt with: the why and the what of the FFC. Why are candidates evaluated by comparison with the FFC rather than the input itself? Comparison with the input would 3 Only markedness constraints make the old/new distinction. Because the FFC has no faith- fulness violations, all faithfulness violations are new, in the sense that they are not shared with the FFC. If F constraints existed, they could never be violated, and so they would O contribute nothing to language typology. Brought to you by | University of California Authenticated Download Date | 11/3/14 10:04 PM 10 John J. McCarthy simplify the theory by eliminating the need for t-correspondence but runs into problems because inputs may lack fully predictable structure, such as syllabification, or they may have it wrong. If so, then every ONSET viola- tion might appear to be new even if, intuitively, it is not. The FFC, unlike the input, is guaranteed to be fully formed, and so its markedness viola- tions can be sensibly compared to those of any other candidate. (Also see McCarthy (2002a) and Jun (2002) for parallel discussion of this point. Interestingly, Jun demonstrates a need for the FFC in a very different domain, positional faithfulness.) Every candidate set emitted by GEN contains a fully faithful candidate (FFC). This assumption is more or less implicit in the basic statements of OT, it is a necessary consequence of correspondence theory, and it is made explicit in Moreton (1996/1999). By definition, the FFC obeys every faith- fulness constraint. In correspondence terms, the relation (cid:1) between the input and the FFC is one-to-one, onto, and order-preserving (MAX, DEP, LINEARITY, INTEGRITY, and UNIFORMITY are all obeyed) with only identi- cal elements standing in correspondence (all IDENT(feature) constraints are obeyed). A candidate set may contain more than one candidate that is fully faithful in this sense. Phonological properties that are universally non- contrastive are not governed by faithfulness constraints, so candidates that differ only in these properties are equivalent, faithfulness-wise. The obvious example is tautomorphemic syllabification, which is claimed never to be contrastive (Blevins 1995: 221, Clements 1986: 318, Hayes 1989: 260). An unsyllabified input like /maba/ or a syllabified input like /mab.a/ will be associated by GEN with many faithful and fully syllabified candidates: m.a.b.a, ma.b.a, m.a.ba, m.aba, m.ab.a, ma.ba, mab.a, maba. But to evaluate comparative markedness constraints, a unique FFC is required. A proposal for finding a unique FFC is made in McCarthy (2002a). It selects as FFC the faithful candidate that is, in effect, the most harmonic, using a procedure that is reminiscent of lexicon optimization (Prince and Smolensky 1993). Because space is limited, I am not able to present that proposal here; this lacuna will not interfere with the arguments in this article, however, since only contrastive properties are involved in the comparative constraints under discussion. Brought to you by | University of California Authenticated Download Date | 11/3/14 10:04 PM