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Figure from:Head–dependent asymmetries in phonology: complexity and visibility

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Some complexity HDAs at the phonological phrase level are schematically illustrated in (29). Example (29a) illustrates a language where the word that occupies the head of phrase, say the rightmost word in a phrase, may have a degree of complexity greater than that permitted to phrase-interna words. For example, the head word, but not the dependent words, might be required, as in (29a), to consist of at least two feet; or, in the non-loca version of this HDA in (29b), the head word might be required to have at least a branching foot, i.e. a foot dominating two moras, a degree o structural complexity not required of (or allowed to) dependents: Example (29b) in fact illustrates the typical case of minimal worc requirements found in many languages, whereby a word must have ¢ certain complexity (McCarthy & Prince 1990). Such requirements are typically imposed on content words, i.e. words that can be the heads oi maximal projections; other words, such as function words, 1.e. word: belonging to certain closed classes, are often excluded from these require- ments. For example, a minimal word in Old English must have at least twe moras, a requirement that is imposed on major class words such as nouns e.g. scip ‘ship’, s@: ‘sea’, *sci, *se, verbs and adjectives (30a); however

Figure 7 Some complexity HDAs at the phonological phrase level are schematically illustrated in (29). Example (29a) illustrates a language where the word that occupies the head of phrase, say the rightmost word in a phrase, may have a degree of complexity greater than that permitted to phrase-interna words. For example, the head word, but not the dependent words, might be required, as in (29a), to consist of at least two feet; or, in the non-loca version of this HDA in (29b), the head word might be required to have at least a branching foot, i.e. a foot dominating two moras, a degree o structural complexity not required of (or allowed to) dependents: Example (29b) in fact illustrates the typical case of minimal worc requirements found in many languages, whereby a word must have ¢ certain complexity (McCarthy & Prince 1990). Such requirements are typically imposed on content words, i.e. words that can be the heads oi maximal projections; other words, such as function words, 1.e. word: belonging to certain closed classes, are often excluded from these require- ments. For example, a minimal word in Old English must have at least twe moras, a requirement that is imposed on major class words such as nouns e.g. scip ‘ship’, s@: ‘sea’, *sci, *se, verbs and adjectives (30a); however

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In such theories, the basic units are unary features or ‘elements’ that can occur separately or in combination (for further development of this idea see van der Hulst 1994). As shown, mid vowels are branching under this view, and more complex than the other vowels. In the above example, then, the generalisation is that vowels with branching structures are permitted only in stressed syllables. In order to be able to classify this as a case of a non-local complexity asymmetry, we need a theory of segmental representation which ranks the three peripheral vowels as less complex than the two mid vowels. Most theories which view vowels as being composed of combinations of basic particles or elements — versions of dependency phonology (Anderson & Ewen 1987), particle phonology (Schane 1984) and government phonology (Kaye et al. 1985) — have this property, as shown in the minimal repre- sentations in (6):
In such theories, the basic units are unary features or ‘elements’ that can occur separately or in combination (for further development of this idea see van der Hulst 1994). As shown, mid vowels are branching under this view, and more complex than the other vowels. In the above example, then, the generalisation is that vowels with branching structures are permitted only in stressed syllables. In order to be able to classify this as a case of a non-local complexity asymmetry, we need a theory of segmental representation which ranks the three peripheral vowels as less complex than the two mid vowels. Most theories which view vowels as being composed of combinations of basic particles or elements — versions of dependency phonology (Anderson & Ewen 1987), particle phonology (Schane 1984) and government phonology (Kaye et al. 1985) — have this property, as shown in the minimal repre- sentations in (6):
A syntagmatic local asymmetry is illustrated in (9): In this example, heads and dependents may both branch, so there is no paradigmatic asymmetry; however, in any given structure, the dependent (D) may not be more complex than the head (H). Thus, (9c) is ruled out. The Greek example above illustrates a paradigmatic HDA: the complex vowels /e/ and /o/ can appear in a stressed syllable, but not in an unstressed syllable. A syntagmatic version of this HDA would occur in a language in which mid vowels may occur in an unstressed syllable, but not when the stressed vowel is high.®
A syntagmatic local asymmetry is illustrated in (9): In this example, heads and dependents may both branch, so there is no paradigmatic asymmetry; however, in any given structure, the dependent (D) may not be more complex than the head (H). Thus, (9c) is ruled out. The Greek example above illustrates a paradigmatic HDA: the complex vowels /e/ and /o/ can appear in a stressed syllable, but not in an unstressed syllable. A syntagmatic version of this HDA would occur in a language in which mid vowels may occur in an unstressed syllable, but not when the stressed vowel is high.®
When a verb or noun has a coordinate complement immediately to its right, the phrasing usually groups the first member of the compound with the preceding governor, as in (15). This type of phrasing is consistent with putting a phrase boundary at the right edge of X™*: the first such edge in (15) coincides with the end of the first NP of the complement. between the PP and the V (with cliticisation of the preposition to th following noun).
When a verb or noun has a coordinate complement immediately to its right, the phrasing usually groups the first member of the compound with the preceding governor, as in (15). This type of phrasing is consistent with putting a phrase boundary at the right edge of X™*: the first such edge in (15) coincides with the end of the first NP of the complement. between the PP and the V (with cliticisation of the preposition to th following noun).
normally be divided into two phrases forms a single phrase when it consists of only two words. In this connection, compare (16a) and (16b).
normally be divided into two phrases forms a single phrase when it consists of only two words. In this connection, compare (16a) and (16b).
Let us consider now how we might account for phenomena like the Division Rule. We observe first that it involves an asymmetry between a head phonological phrase and dependent phonological phrases in terms of how much complexity each allows. This asymmetry, however, goes exactly the wrong way: the head phonological phrase allows for less complexity than dependent phrases do, as it made clear by (21): Although (21) accurately characterises the facts, it does not explain why such an asymmetry should exist. We propose that there is another way of looking at the Division Rule which allows us to better understand its rationale. As a first step, we observe that in prominent prosodic positions, it is as if the branching at the foot level counts as if it were branching at the word level. Thus, a word with two feet counts as if it is two words, exhausting its phonological phrase. A formal characterisation of just such
Let us consider now how we might account for phenomena like the Division Rule. We observe first that it involves an asymmetry between a head phonological phrase and dependent phonological phrases in terms of how much complexity each allows. This asymmetry, however, goes exactly the wrong way: the head phonological phrase allows for less complexity than dependent phrases do, as it made clear by (21): Although (21) accurately characterises the facts, it does not explain why such an asymmetry should exist. We propose that there is another way of looking at the Division Rule which allows us to better understand its rationale. As a first step, we observe that in prominent prosodic positions, it is as if the branching at the foot level counts as if it were branching at the word level. Thus, a word with two feet counts as if it is two words, exhausting its phonological phrase. A formal characterisation of just such
Our claim is that where there is a difference between a head and its dependents with respect to visibility, constituent units of the head are visible to a greater depth than the corresponding constituents of the Tiberian Hebrew thus involves a second type of HDA. In general terms, this type of HDA involves the degree to which a phonological process which applies to a node C has access to the internal structure of its daughters. In (23), we will say that C is (relatively) transparent if it allows access to nodes of type E, and opaque if nothing can be ‘seen’ below the level of D:
Our claim is that where there is a difference between a head and its dependents with respect to visibility, constituent units of the head are visible to a greater depth than the corresponding constituents of the Tiberian Hebrew thus involves a second type of HDA. In general terms, this type of HDA involves the degree to which a phonological process which applies to a node C has access to the internal structure of its daughters. In (23), we will say that C is (relatively) transparent if it allows access to nodes of type E, and opaque if nothing can be ‘seen’ below the level of D:
minor class words (we ‘we’, se ‘that’, hwa ‘who ?’) may escape it, so that the words in (30b) are permissible:
minor class words (we ‘we’, se ‘that’, hwa ‘who ?’) may escape it, so that the words in (30b) are permissible:
In the Italian example, the units that are mapped onto the timing plane are words in dependent position, but daughters of words, 1.e. feet, in head position. Vis-a-vis the mapping, then, it is as if heads are ‘magnified’. This is the nature of visibility asymmetries: heads may be magnified in this way relative to dependents, but dependents may not be magnified relative to heads:
In the Italian example, the units that are mapped onto the timing plane are words in dependent position, but daughters of words, 1.e. feet, in head position. Vis-a-vis the mapping, then, it is as if heads are ‘magnified’. This is the nature of visibility asymmetries: heads may be magnified in this way relative to dependents, but dependents may not be magnified relative to heads:
[here is a mapping between the word plane and prosodic structure.”' Chus, our diagram (37) above should be augmented as in (40): The terminal elements of prosodic structure, we assume, are line 0 units that do the work that in other theories is attributed to moras (w). On this interpretation, feet dominate moras directly, syllables being in another plane. Between the word plane and the prosodic plane a mapping relation exists whereby line 0 units correspond either to rhymes (QI) or to daughters of rhymes (QS). It follows, then, that if a QS/QI asymmetry exists, we expect to find that dependent feet are built on line 0 units that correspond to complete rhymes, whereas head feet are built on daughters of the rhyme, as shown in (41): We assume that the syllabic organisation of segments is represented in a separate word plane. This plane is distinct from the prosodic plane.”° The word plane consists of a sequence of syllables that forms a word:
[here is a mapping between the word plane and prosodic structure.”' Chus, our diagram (37) above should be augmented as in (40): The terminal elements of prosodic structure, we assume, are line 0 units that do the work that in other theories is attributed to moras (w). On this interpretation, feet dominate moras directly, syllables being in another plane. Between the word plane and the prosodic plane a mapping relation exists whereby line 0 units correspond either to rhymes (QI) or to daughters of rhymes (QS). It follows, then, that if a QS/QI asymmetry exists, we expect to find that dependent feet are built on line 0 units that correspond to complete rhymes, whereas head feet are built on daughters of the rhyme, as shown in (41): We assume that the syllabic organisation of segments is represented in a separate word plane. This plane is distinct from the prosodic plane.”° The word plane consists of a sequence of syllables that forms a word:
4.2 The main stress first syndrome The asymmetry is as expected: mapping from the word plane to the prosodic plane may not refer to daughters of dependents unless they also refer to daughters of heads. Hence, the contrary situation, where secondary stress is sensitive to quantity while main stress is not, is ruled out, since it would require non-heads to be sensitive to a distinction that is not available to the head:
4.2 The main stress first syndrome The asymmetry is as expected: mapping from the word plane to the prosodic plane may not refer to daughters of dependents unless they also refer to daughters of heads. Hence, the contrary situation, where secondary stress is sensitive to quantity while main stress is not, is ruled out, since it would require non-heads to be sensitive to a distinction that is not available to the head:
The handshapes that may be selected are unmarked. According to Battison (1974: 6—7) (and cf. Sandler 1995), these handshapes: balanced signs both hands have equal specification for all class nodes. In unbalanced signs, the strong hand is fully specified for the class nodes, but this is not the case for the weak hand. It is a striking fact that if the handshapes differ, the weak hand has a choice from a very limited set (at least among the most frequent cases):
The handshapes that may be selected are unmarked. According to Battison (1974: 6—7) (and cf. Sandler 1995), these handshapes: balanced signs both hands have equal specification for all class nodes. In unbalanced signs, the strong hand is fully specified for the class nodes, but this is not the case for the weak hand. It is a striking fact that if the handshapes differ, the weak hand has a choice from a very limited set (at least among the most frequent cases):