Optimality theory is a theory of constraint interactions. Constraints express generalisations about the grammatical structure of a given language. Con-straints are invariant across languages and cross-linguistic variation derives from the differences in ranking only. There are two basic types of constraints.
Markedness constraints define the well-formedness of the output representa-tions, whereas faithfulness constraints regulate the mapping of the underlying forms onto surface representations. Markedness constraints are typologically and/or functionally motivated. For instance, the constraint NoCoda (‘Syllables may not have codas’) reflects the cross-linguistic preference for open syllables.2 It is also phonetically grounded because coda consonants lack strong perceptual cues. Faithfulness constraints refer to both the input and the output. They reg-ulate the preservation of lexical contrast in output forms by requiring the input and the corresponding output forms to be identical. Faithfulness is violated by both deletion and insertion, as well as by featural change, coalescence, order change, etc. Markedness constraints and faithfulness constraints are inherently in conflict. That is, the reduction in markedness entails violation of faithful- ness. Conversely, the preservation of faithfulness leads to an increase in mark-edness. Languages differ in their resolution of conflicts between markedness and faithfulness. For example, coda consonants occur in a language in which the markedness constraint NoCoda is outranked by the faithfulness constraint Maxseg prohibiting segment deletion. In languages with the reverse ranking, NoCoda >> Maxseg, syllables are open (the symbol ‘>>’ indicates domi-nance relation).
The language-specific ranking of constraints constitutes the grammar of a given language. Besides constraints and their rankings, the OT grammar contains GEN (for generator), which produces a set of possible output forms for each input. Another component of the grammar, EVAL (for evaluation), assesses the possible candidates: the output that incurs the least costly violation of the constraints is selected as optimal. Schematic representation of the func-tions of GEN and EVAL are provided below.
(1) GEN //inputi// → (cand1, cand2, cand3, …candn) EVAL (cand1, cand2, cand3, …candn) → [outputi]
2 In contrast to the mainstream OT, constraints pertaining to phonotactic structure can be viewed not as absolute requirements, but as preferences (cf. Dziubalska-Kołaczyk, 2001).
Constraints operate on surface representations, selecting the most optimal out- put from an infinite set of possible forms generated by the grammar. The evalu-ation of possible outputs is displayed in a tableau, as demonstrated in (2) below.
Constraints are listed from left to right, with a solid vertical line indicating a domination order. The input is usually shown in the upper left-hand corner, while possible outputs are listed on the left-hand side of the tableau. A candi-date which incurs a violation of the constraint heading the column is marked with ‘*’, whereas a blank cell indicates that a given constraint is satisfied. The exclamation mark ‘!’ means that a candidate fatally violates the constraint and is eliminated from further consideration. The correct winner is shown with an arrow.
(2) i. Languages allowing coda consonants
//tat// Maxseg NoCoda
⇒ a. tat *
b. ta *!
ii. Languages disallowing coda consonants
//tat// NoCoda Maxseg
⇒ a. ta *
b. tat *!
All the outputs shown in the tableaux above incur a violation of some con-straint. In (2i), Maxseg prefers the faithful candidate (2ia), whereas NoCoda chooses its unmarked competitor in (2ib). Candidate (2ia) comes out optimal because Maxseg dominates NoCoda. The opposite ranking in (2ii) selects candi-date (2iia) which satisfies the NoCoda by deleting the final consonants.
Classic OT assumes that inputs are mapped onto the outputs directly, without intermediate stages. This principle, dubbed parallelism, is one of the most controversial and frequently contended aspects of OT. Since its inception, OT research has accumulated a massive body of evidence proving the inade-quacy of parallel evaluation in dealing with opacity. Several attempts have been made to resolve this issue without forfeiting the principle of strict parallelism;3
3 The auxiliary theories include sympathy theory (McCarthy, 1999; McCarthy, 2003), output- output constraints (Kraska-Szlenk, 1995; Benua, 1997), targeted constraints (Wilson, 2001), lexically-indexed constraints (Pater, 2000), candidate chains (McCarthy, 2007), among others.
however, all of them have proven unsatisfactory for various reasons.4 The opac-ity problem does not arise in the serial version of OT adopted in the present study (Inkelas & Orgun, 1995; Kiparsky, 1997, 2000; Rubach, 1997, et seq.;
Bermúdez-Otero, 1999, 2003; Ito & Mester, 2001, 2003). The principle differ-ence between standard OT and serial OT (called Derivational OT, Stratal OT, or LP/OT) is that the latter admits intermediate levels of derivation, each of which contains a separate constraint ranking. The evaluation of candidates proceeds in stages, with the output at leveln constituting the input at leveln+1. There is a general agreement that the number of levels/strata should be kept to a minimum, and should reflect the differences between stem, word and phrase phonology.
Slavic languages with their complex morphological structure provide a strong argument for the derivational levels in phonology. Rubach (1997, et seq.) demonstrates that the assumption of a serial evaluation of the candidate forms allows for a more insightful analysis of numerous opaque processes in various Slavic languages, including palatalization, glide insertion, yer vocalisation, or syllabification. A particularly convincing piece of evidence for level distinction comes from Russian, which has two contradictory processes, [i]-palatalization and [i]-retraction (Rubach, 2000a). The former palatalises hard consonants before the front vowel [i], whereas the latter retracts [i] after hard consonants.
The two processes operate on segmentally identical inputs in different morpho-syntactic contexts: palatalisation applies inside words, and retraction applies at word boundaries e.g. bratiška //brat+iška// → [bratjiškә] ‘brother’ (dim.) vs.
brat Iška //brat#iška// → [bratɨškә] ‘brother Iška (proper name)’.5 Parallel OT cannot generate the forms [bratj iškә] and [bratɨškә] with one set of ranked con-straints, and Rubach (2000a) argues that the problem can only be solved if OT admits two distinct phonological modules corresponding to the lexical and the post-lexical levels in Lexical Phonology (Kiparsky, 1982). The data from East Slavic dialects discussed in Chapters 5 and 6 of this book furnishes fur-ther motivation for level distinction. For instance, we demonstrate in Chapter 5 that an interaction of vowel neutralisation and [e]-retraction which produces opaque forms such as vedjom //vjeˈdj+em// [vjiˈdjom] ‘lead’ (1st pers. pl. pres.) vs. medvedjom //mjedvjeˈdj+om// [mjɪdvjaˈdj om] ‘bear’ (instr. sg), is straightfor-wardly accounted for in the model assuming that vowel neutralisation is a level 1 process and [e]-retraction is a level 2 process.
4 See, for example, Rubach (2000b) and McCarthy (2007) for a review and critique of different approaches to opacity within OT.
5 Here and below, ‘+’ stands for a morpheme boundary and ‘#’ indicates a word boundary.