11.2.2 Templatic Morphology

Finite-state models of phonology and morphology have also been proposed for the templatic (non-concatenative) morphology (discussed on page ??) common in Semitic languages like Arabic, Hebrew, and Syriac.

There are a number of computational finite-state implementations of non-concatenative morphology. Many of them draw on the the CV approach of McCarthy (1981), in which a word like /katab/ is represented by three separate morphemes; a root morpheme consisting of consonants (ktb), a vocalic morpheme consisting of vowels (a), and a CV

pattern morpheme (sometimes called a binyan or a CV skeleton) (CVCVC). McCarthy represented this morphemes on three separate morphological tiers (Goldsmith, 1976).

An influential model by Kay (1987), for example, uses separate tapes for each of McCarthy's tiers. A high-level intuition of Kay's model is shown in Fig. 11.7, which shows his special transducer that reads four tapes instead of two.

The complication with such a multi-tape model is designing a machine which aligns the various strings on the tapes in the correct way; Kay proposed that the binyan tape could act as a sort of guide for alignment. Kay's intuition has led to a number of more fully worked out finite-state models of Semitic morphology; see the end of the chapter for details of these models, as well as alternatives based on new finite-state operations.

11.3 COMPUTATIONAL OPTIMALITY THEORY

In a traditional phonological derivation, we are given an underlying lexical form and a surface form. The phonological system then consists of a sequence of rules which

map the underlying form to the surface form. Optimality Theory (OT) (Prince and Smolensky, 1993) offers an alternative way of viewing phonological derivation, based on the metaphor of filtering rather than transforming. An OT model includes two functions (GEN and EVAL) and a set of ranked violable constraints (CON). Given an underlying form, the GEN function produces all imaginable surface forms, even those which couldn't possibly be a legal surface form for the input. The EVAL function then applies each constraint in CON to these surface forms in order of constraint rank. The surface form which best meets the constraints is chosen.

Let’s briefly introduce OT, using some Yawlemani data, and then turn to the computational ramifications. $ ^6 $ In addition to the interesting vowel harmony phenomena discussed above, Yawlemani has phonotactic constraints that rule out sequences of consonants; three consonants in a row (CCC) are not allowed to occur in a surface word. Sometimes, however, a word contains two consecutive morphemes such that the first one ends in two consonants and the second one starts with one consonant (or vice versa). What does the language do to solve this problem? It turns out that Yawlemani either deletes one of the consonants or inserts a vowel in between.

If a stem ends in a C, and its suffix starts with CC, the first C of the suffix is deleted ("+" here means a morpheme boundary):

C-deletion: C $ \rightarrow \epsilon / C + \_\_ C $

For example, simplifying somewhat, the CCVC “passive consequent adjunctive” morpheme hne:l drops the initial C if the previous morpheme ends in a consonant. Thus after diyel “guard”, we would get the form diyel-ne:l-aw, “guard - passive consequent adjunctive - locative”.

If a stem ends in CC and the suffix starts with C, the language instead inserts a vowel to break up the first two consonants:

V-insertion: $ \epsilon \to \mathrm{V} / \mathrm{C} \xrightarrow{\quad} \mathrm{C} + \mathrm{C} $

For example in i is inserted into the root ?ilk- “sing” when it is followed by the C-initial suffix -hin, “past”, producing ?ilik-hin, “sang”, but not when followed by a V-initial suffix like -en, “future” in ?ilken “will sing”.

Kisseberth (1970) proposed that these two rules have the same function: avoiding three consonants in a row. Let's restate this in terms of syllable structure. It happens that Yawelmani syllables can only be of the form CVC or CV; complex onsets or complex codas i.e., with multiple consonants, aren't allowed. Since CVCC syllables aren't allowed on the surface, CVCC roots must be resyllabified when they appear on the surface. From the point of view of syllabification, then, these insertions and deletions all happen so as to allow Yawelmani words to be properly syllabified. Here's examples of resyllabifications with no change, with an insertion, and with a deletion:

The intuition of Optimality Theory is to try to directly represent these kind of constraints on syllable structure directly, rather than using idiosyncratic insertion and deletion rules. One such constraint, $ *COMPLEX $, says “No complex onsets or codas”. Another class of constraints requires the surface form to be identical to (faithful to) the underlying form. Thus FAITHV says “Don’t delete or insert vowels” and FAITHCH says “Don’t delete or insert consonants”. Given an underlying form, the GEN function produces all possible surface forms (i.e., every possible insertion and deletion of segments with every possible syllabification) and they are ranked by the EVAL function using these (violable) constraints. The idea is that while in general insertion and deletion are dispreferred, in some languages and situations they are preferred over violating other constraints, such as those of syllable structure. Fig. 11.8 shows the architecture.

The EVAL function works by applying each constraint in ranked order to each candidate. Starting with the highest-ranked constraints, if one candidate either does not violate no constraints or violates less of them than all the other candidates, that candidate is declared optimal. If two candidates tie (have the same highest ranked violation), then the next-highest ranked violation is considered. This evaluation is usually shown on a tableau (plural tableaux). The top left-hand cell shows the input, the constraints are listed in order of rank across the top row, and the possible outputs along the left-most column. $ ^{7} $ If a form violates a constraint, the relevant cell contains *; a *! indicates the fatal violation which causes a candidate to be eliminated. Cells for

constraints which are irrelevant (since a higher-level constraint is already violated) are shaded.

One appeal of Optimality Theoretic derivations is that the constraints are presumed to be cross-linguistic generalizations. That is all languages are presumed to have some version of faithfulness, some preference for simple syllables, and so on. Languages differ in how they rank the constraints; thus English, presumably, ranks FAITHCH higher than *COMPLEX*. (How do we know this?)