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<?xml version="1.0" standalone="yes"?> <Paper uid="E93-1038"> <Title>Formal Properties of Metrical Structure</Title> <Section position="3" start_page="0" end_page="326" type="metho"> <SectionTitle> 2 The definition of a bracketed grid </SectionTitle> <Paragraph position="0"> Below I give a formal definition of the bracketed grid, as it is introduced by HV and subsequently elaborated and revised by these authors and others, most notably \[Hayes, 1991\]. HV have a major part of their book devoted to the formalism themselves, but there are numerous problems with this formalization. I will mention two of them.</Paragraph> <Paragraph position="1"> First, their formalization is not flexible enough to capture all instances of (bracketed) grid theory as it is actually used in the literature of the last few years. They merely give a sketch of the specific implementation of bracketed grid theory as it is used in the rest of their book. Modern work like \[Kager, 1989\] or \[Hayes, 1991\] cannot be described within this framework.</Paragraph> <Paragraph position="2"> Secondly, their way of formalizing bracketing grids has very much a 'derivational' flavour. They are more interested in how grids can be built than in what they look like. Although looking at the derivational aspects is an interesting and worthwile enterprise in itself, it makes their formalism less suitable for a comparison with metrical trees.</Paragraph> <Paragraph position="3"> A grid in the linguistic literature is a set of lines, each line defining a certain subgroup of the stress bearing elements. Thus, in 1 (HV's (85)), the asterisks ('stars') on line 0 represent the syllables of the word formaldehyde, the stars on line 1 secondary stress and line 2 represents the syllable with primary stress:</Paragraph> <Paragraph position="5"> for mal de hyde We can formalize the underlying notion of a line as follows: Definition 1 (Line) A line Liis a pair < At, -'4i> where Ai = {a~,...,a?}, where a~,...,a n are constants, n a fixed number -~i is a total ordering on Ai such that the following axioms hold.</Paragraph> <Paragraph position="6"> a. Vot, 13, 7 ELi : ot ~i 13 A 13 ~i 7 ~&quot; ot -41 7 (transitivity) null b. Vow, 13 ELi : a -4i 13 ::~ -'(13 &quot;~i a) (asymmetry) c. Va G Li : ~(a -41 a) Orreflezivity) We say that Li C Lj if Ai C A#, a ELi if a E At. Other set theoretic expressions are extended in a likewise fashion.</Paragraph> <Paragraph position="7"> Yet this formalisation is not complete for bracketed grids. It has to be supplemented by a theory about the brackets that appear on each line, i.e. by a theory of constituency and by a theory of what exactly counts as a star on a given line.</Paragraph> <Paragraph position="8"> We have exactly one dot on top of each column of stars2.Moreover, each constituent on a line has one star in it plus zero, one or more dots. The stars are heads. HV say that these heads govern their complements. This government relation can only be a relation which is defined in terms of precedence. Suppose we make this government relation into the primitive notion instead of the constituent. A metrical line is defined as a line plus a government relation on that line: Definition 2 (Metrical line) A metrical line MLi is a pair <Li,P~>, where Li is a line Ri is a relation on Li and an element of {-~i,>-i,--,i , ~-'i, '~i} ZThat is, if we follow the current tradition rather than HV.</Paragraph> <Paragraph position="9"> With the following definitions holding3: Definition 3 (Precedence Relations) a Ni 13 C/~ We assume that something like Government Requirement 1 holds, just as it is assumed in HV that every element is in a constituent, modulo extrametricality (which we will ignore here).</Paragraph> <Paragraph position="10"> Government Requirement 1 (to be revised below) A line Limeets the government requirement iff all dots on Li are governed, i.e. a star is in relation Ri to them.</Paragraph> <Paragraph position="11"> Now a constituent can be defined as the domain that includes a star, plus all the dots that are governed by this star. We have to be a little bit careful here, because we want to make sure that there is only one star in each constituent.</Paragraph> <Paragraph position="12"> In a structure like the following we do not want to say that the appointed dot is governed by the first star. It is governed by the second star, which is nearer to it: (2) *...*...</Paragraph> <Paragraph position="13"> T In order to ensure this, we adopt an idea from modern GB syntax, viz. Minimality, which informally says that an element is only governed by another element if there is no closer governor. The definition of Phonological Minimality could look as follows: Definition 4 (phonological government) aGi# (a governs 13 on line i) iff a is a star and art13 A -~37, 7 a star : \[7R/13 A aR/7\] We will give the formal definition of a star later on in this chapter. The government requirement is now to be slightly modified.</Paragraph> <Paragraph position="14"> Government Requirement 2 to be revised below A line Limeets the government requirement iff all dots on Li are governed, i.e. a star in Liis in relation Gi to them.</Paragraph> <Paragraph position="15"> We can now formally define the notion of a constituent 4.</Paragraph> <Paragraph position="16"> aActually, HV also use a fifth kind of constituent in their book, viz. one of the form (. * .). Because there has been a lot of criticism in the literature against this type of government, I will not not discuss it here. 4The reviewer of the abstract for EACL notices that under the present definitions it is not possible to express the kind of ambiguity that is current in (parts of) bracketed grid literature, where it is not sharply defined whether a dot is governed by the star to its left or by the star to its right. This is correct. It is my present purpose to define a version of bracketed grids that comes closest to trees because only in this way we can see which are the really essential differences between the two formalisms. Definition 5 (Constituent) A constituent on a line Li is a set, consisting of exactly one star S in Li plus all elements that are not stars but that are governed by S.</Paragraph> <Paragraph position="17"> We now have a satisfying definition of a metrical line. We can define a grid as a collection of metrical lines, plus an ordering relation on them: Definition 6 (Grid) A grid G is a pair < PS, 1>, where</Paragraph> <Paragraph position="19"> I is a total ordering on PS, such that VLi, Lj * PS : Li I L1 C/~ \[Li C Lj A Va,~3 * Li fl Lj : \[a -~i Z C/~ 8\]\] where C is intended to denote the proper subset relation, so Li C L 1 ~ &quot;,(Li = Li).</Paragraph> <Paragraph position="20"> It is relatively easy to see that I by this definition is transitive, asymmetric and irreflexive. We also define the inverse operator T such that Li T L 1 iff Lj ILi.</Paragraph> <Paragraph position="21"> The most interesting part of definition 6 is of course the 1 ('above')-relation. Look at the grid in (3) (= HV's (77), p. 262): (3) line 3 (. .) line 2 (. .) (.) line 1 Ten ne see Each of the lines in this grid is shorter than the one immediately below it, in that it has fewer elements. This follows from elementary pretheoretical reasoning. Every stressed syllable is a syllable, every syllable with primary stress also has secondary stress. We expressed this in definition 6 by stating that every line is a subset of the lines below it. By this statement we also expressed the idea that the elements represented on the higher line are in fact the same things as those represented on the lower lines, not just features connected of these. The second part of the definition says that the relative ordering of the elements in each line is the same as that on the other lines.</Paragraph> <Paragraph position="22"> Our present definition of a metrical grid already has some nice properties. For example, the Continu- null ous Column Constraint, which plays a crucial role as an independent stipulation in \[Hayes, 1991\] can be derived from definition 6 as a theorem: (4) Continuous Column Constraint (CCC): A grid containing a column with a mark on layer (=our metrical line) n+l and no mark on layer n is ill-formed. Phonological rules are blocked when they would create such a configuration.</Paragraph> <Paragraph position="23"> The CCC excludes grids like (5), where b is present on the third line, but not on the second.</Paragraph> <Paragraph position="24"> (5) a b a c d abed We can formalize the CCC as a theorem in our system: null Theorem 1 (CCC)VaVLiLj : (a E Li ALi \].</Paragraph> <Paragraph position="25"> e Proof of theorem 1 Suppose a E Li, suppose Li I Lj. Then (by (13)) L, C Lj. Now the standard definition of C implies VX : X ELi -&quot;* X E Lj. Instantiation of X by c~, our first assumption and Modus Ponens give a E Li.O We can also easily define the notion of a dot and a star, informally used in the above definitions of be revised below A grid G meets the government requirement iff all lines in G meet the government requirement. null We want to introduce an extra requirement on grids. Nothing in our present definition excludes grids consisting of infinitely many lines. However, in our linguistic analyses we only consider finite construetions. We need to express this. First, we define the notions of a top line and a bottom line. Then we say that a finite grid always has one of each.</Paragraph> <Paragraph position="26"> Definition 8 (Top line and bottom line) For a certain grid G, VLi E G (LToP, G = Li)d--efVLj E G : \[(Li = Lj) V (Li ~ Lj)\] (LBoTTOM,G -&quot; LI)~'~fVLj * G : \[(ni = Lj)V(Lj 1 Li)\] Definition 9 (Finite grid) A grid G is called a finite grid if 3Li * G: \[Li= LTOP, G\] A 3Lj * G : \[L i = LBoTTOM,e\] Note that we have to say something special with regard to the government relation in LTOP, G. By definition, this line has only dots in it, so it always looks as something like (6).</Paragraph> <Paragraph position="27"> (6) .......</Paragraph> <Paragraph position="28"> There can be no star on this level. A star by definition has to be present at some higher line and there is no higher line above LTOP, G. This means that the LTOP, G can never be meeting the government requirement and that in turn means that no linguistic grid can ever meet the government requirement. In order to avoid this rather unfortunate situation, we have to slightly revise the definition of meeting the government requirement for linguistic grids. Government P~quirement 5 (for grids) -- final version A grid G meets the government relation iff all the lines Li E G - {LTop, a} meet the government requirement.</Paragraph> <Paragraph position="29"> Definition 10 (Linguistic grid) A linguistic grid is a finite grid which meets the government relation A last definition may be needed here. If we look at the grids that axe actually used in linguistic theory, it seems that there is always one line in which there is just one element. Furthermore, this line is the top line (the only line that could be above it would be an empty line, but that one doesn't seem to have any linguistic significance).</Paragraph> <Paragraph position="30"> This observation is phrased in \[Hayes, 1991\] as follows: if prominence relations are obligatorily defined on all levels, then no matter how many grid levels there are, there will be a topmost level with just one grid mark.</Paragraph> <Paragraph position="31"> We can formalize this ~s follows: Definition 11 (Complete linguistic grids) A linguistic grid G is called a complete linguistic grid iff \[LToP, G\] = 1, i.e. 3a : \[a E LTOP, G A Vfl : L 8 e LTOP, G ::~ # ---- O~\]\] We call this type of grid complete because we can easily construct a complete linguistic grid out of every linguistic grid.</Paragraph> <Paragraph position="32"> If LTOP, G is non-empty, we construct a complete grid by projecting the rightmost (or alternatively the leftmost) element to a new line L/and by adding the government requirement ~- (or -4) to LTOP, G. Finally we add the relation Lil LTOP, G to the grid, i.e. we make Lito the new LTOP, G.</Paragraph> <Paragraph position="33"> If the top line of the grid is empty, we remove this line from the grid and proceed as above. Most linguistic grids that are known from the literature, are complete.</Paragraph> <Paragraph position="34"> Some authors impose even more restrictions on their grids. I believe most of those claims can be expressed in the formal language developed in this section. One example is \[Kager, 1989\], who claims that all phonological constituents are binary. This Binary Constituency Hypothesis can be formulated by replacing definition 2: Definition 12 A metrical line MLI is a pair < Li,Ri>, where Li is a line Ri is a relation on Li and an element of {~i, ~i} 3 Grids and trees In this section, we will try to see in how much bracketed grids and trees are really different formal systerns, i.e. to what extent one can say things in one formalism that are impossible to state in the other. First recall the standard definition of a tree (we cite from \[Partee et al., 1990\])5: Definition 13 (Tree) A (constituent structure) tree is a mathematical configuration < N, Q, D, P, L >, where N is a finite set, the set of nodes Q is a finite set, the set of labels D is a weak partial order in N x N, the dominance relation P is a strict partial order in N x N, the precedence relation L is a function from N into Q, the labeling function and such that the following conditions hold: (a) 3a E N : V/~ G N : \[<a,/~>E O\] (Single root condition) (b) W,a ~ N : \[(<~,~>~ PV <a,~>E P) C/* (<</Paragraph> <Paragraph position="36"> It is clear that bracketed grids and trees have structures which cannot be compared immediately.</Paragraph> <Paragraph position="37"> Bracketed grids are pairs consisting of a set of complex objects (the lines) and one total ordering relation defined on those objects (the above relation).</Paragraph> <Paragraph position="38"> Trees on the other hand are sets of simple objects (the nodes) with two relations defined on them (dominance and precedence). These simply appear to be two different algebra's where no isomorphism can be defined.</Paragraph> <Paragraph position="39"> Yet if we decompose the algebraic structure of the lines, we see that there we have sets of simple objects (the elements of the line) plus two relations defined on them. One of those relations ('~i) is a strict partial order, just like P. The other relation, Gi, vaguely reminds us of dominance.</Paragraph> <Paragraph position="40"> Yet a line clearly is not a tree. Although -4i has the right properties, it is not so sure that Gi does.</Paragraph> <Paragraph position="41"> While this relation clearly is asymmetric (because it is directional), it is not a partial order.</Paragraph> <Paragraph position="42"> First of all, it is not transitive. (7) is a counterexample. null</Paragraph> <Paragraph position="44"> Here aGib and bGie but not aGie, because of minimality (there is a closer governor, viz. b). Gi also 5For the moment, we will not consider Q and L, because these are relatively unimportant for our present aim and goal and there is nothing comparable to the labeling function in our definition of bracketed grids. This is to say that for now we will study unlabeled trees. Notice however that the trees actually used in the phonological literature do use st least a binary set of labels { s, w } is irreflexive, of course, because no element is to the left or to the right of itself.</Paragraph> <Paragraph position="45"> A more interesting relation emerges if we consider the grid as a whole. Because trees are finite structures, we need to consider linguistic grids only. The line LBOTTOM,G has the property that VaVLI ~ G : \[a ~Li =~ ~ ~ LBOTTOM,G\]. This follows from the definitions of LBOTTOM,G and of the 'above' relation. null This means that all basic elements of the grid are present on LBOTTOM,G and, as we have seen above, we can equal P to &quot;~BOTTOM,G. Furthermore, we can build up a 'supergovernment' relation {7, which we define as the disjunction of all government rela- null Again, we exclude the government relation of the two stars in (7).</Paragraph> <Paragraph position="46"> If we want to compare {7 to dominance, we have to make sure it is a partial order. However, {7 obviously still is irreflexive. It also is intransitive. Consider the following grid for example.</Paragraph> <Paragraph position="47"> In this grid a{Tc A c{Td but --,a{Td. For this reason, we take the transitive and reflexive closure of {7, which we call 7&quot;7C/{7.</Paragraph> <Paragraph position="48"> LFrom this, we can define the superline of a linguistic grid 6.</Paragraph> <Paragraph position="49"> Definition 15 (Superline) The superline S/~ of a linguistic grid G is the tuple < ABOTTOM,G, &quot;~BOTTOM,G, &quot;Jf'T~{TG >. The superline is an entity which we can formally compare to a tree, with -~BOTTOM,G = P, ABOTTOM,G = N, 7&quot;T~{7 = D. Of most interest are the complete linguistic grids, firstly because these are the ones that seem to have most applications in linguistc theory and secondly because the requirement that they be complete (i.e. their LTOP, G should have exactly one element) mirrors the single root condition on trees. From now on, we will use the abbreviation CLG for 'complete linguistic grid'. Note that we also restrict our attention to grids which meet the government requirement, i,e. to linguistic grids. We are not so sure that this restriction is equally well supported by metrical theory as the restriction to completeness. However, the restriction 6The superfine itself has no specific status in linguistic theory. I also do not claim it should have one. The superfine is a formal object we construct here because it is the substructure of the bracketed grid that comes closest to a tree.</Paragraph> <Paragraph position="50"> to linguistic grids makes sure that all elements in the grid participate in the government relation, because everything ends as a star somewhere and hence has to be governed by another element.</Paragraph> <Paragraph position="51"> In order to somewhat simplify our proofs below, we introduce one new notational symbol here: ~.</Paragraph> <Paragraph position="52"> Definition l6 (Top Line)V~ E AVLi ~ G : \[c~Li C/~ c~ ~ Li A -,~Lj \[a ~ Lj A L~ ~ Li\]\] This symbol '_~' 'top line' denotes the highest line on which a certain element is present. If a ~ Li, then Liis the highest line at which a can be found. By definition, this means that ~ is a dot on Li.</Paragraph> <Paragraph position="53"> Of course, for every element in a linguistic grid there is one specific top line.</Paragraph> <Paragraph position="54"> We now prove: Theorem 2 For every linguistic grid G, ifG is complete, then SLG satisfies the Single Root Condition. Proof of theorem 2: Consider a complete linguistic grid G. We have to prove that 3a E A : V~ E A : \[< a,/3 >E &quot;/-T~{TG\] (for shortness, we will refer here and in the following to ABOTTOM,G as A and to &quot;~BOTTOM,G as &quot;~ where no confusion arises). Consider the (single) element of LTOP.a. We call this element 7 and prove that V/~ E A : I<7,/~>E TT~gG\]. (Reductio ad absurdum.) Suppose 3/~ E A : \[< 7,/~>~ TT~{Ta\]. Because this/~ is in A, 3Li : ~_ELi\]. We now take the highest/3 for which this condition TT~{TG holds, because delta is on a higher line than /3 and we assumed /3 was the highest element for which this condition did not hold.</Paragraph> <Paragraph position="55"> But now we have < 6, fl >E q'T~{TaA < 3', 6 >E TT~{TG and because TT~{Tais transitive, < %/3 >E &quot;/'7~{7G. This is a contradiction with our initial assumption. \[\] So superlines have one important characteristic of trees. Yet exclusivity and nontangling still do not hold for superlines of CLGs, even if they meet the government requirement.</Paragraph> <Paragraph position="56"> A counter example to exclusivity is (9), where a -~ bA <a,b>E TT~{TG.</Paragraph> <Paragraph position="57"> The reason why these conditions do not hold is that, on lines as well as on superlines, elements can both govern and precede another element. Exclusivity and nontangling are meant to keep precedence and domination apart.</Paragraph> <Paragraph position="58"> Sometimes in the literature on trees (e.g. Sampson 1975) we find some weakening of the definition of a tree, in which exclusivity and nontangling are replaced by the Single mother condition.</Paragraph> <Paragraph position="59"> We first define the mother relation, which is im- null We can now prove: Theorem 3 For every grid G, if G is a CLG then Sf.G satisfies the Single Mother Condition.</Paragraph> <Paragraph position="60"> Proof of theorem 3: (By RAA.) Suppose a,/9, 7 * SPSG and aM/9 A 7M/9 A a # 7- If aM/9, then by definition 19, < a,/9>* ~Ta, and if 7M/9, similarily <7,/9>6 TONG. Because a # 7, we have a # /9.</Paragraph> <Paragraph position="61"> For if a =/9, we would have 7Ma A aM~9. But by (19) we then cannot have 7M/9. A similar line of reasoning shows that/9 ~ 7. So a C/ 7 A 7 C//9. By (17) this means that \[< a,/9>6 ~GA < 7, ~ >6 Ca\], because 7ZQG is the transitive closure of GG. We have reached the following proposition: Proposition 1 The mother relation equals ~ on superlines: V~/9 * SfG : \[otMfl =~< a,/~>6 ~G\] Definition 14 says that if < a,/9>* fig there is a line L/such that aGi/gAdoti(~)}. Also, if < %/9 >* Ga there is a line Ljsuch that 7Gj/gAdob(#)}. Because can by definition be a dot at exactly one line, Li= Ljand otGi/9 and 7Gi/9. However, from the minimality definition of government (4), it follows that in that case (~ = 7. Which is a contradiction. \[\]</Paragraph> </Section> <Section position="4" start_page="326" end_page="327" type="metho"> <SectionTitle> 4 Dependency Trees </SectionTitle> <Paragraph position="0"> Let us summarize the results so far. We have seen that from bracketed grids we can extract sup*tithes, on which the government relations of the normal lines are conflated.</Paragraph> <Paragraph position="1"> These superlines are equivalent to some sort of unlabeled trees, under a very weak definition of the latter notion. Whereas the minimal restrictions of the Single Root Condition and the Single Mother Condition do hold, the same is not necessarily true for the Exclusivity Condition and the Non-Tangling Condition. null It can be shown that in the linguistic literature a form of tree occurs that is exactly isomorphic to bracketed grids. These are the trees that are used in Dependency Phonology.</Paragraph> <Paragraph position="2"> We did not yet discuss what the properties of these trees are. This is what we will briefly do in the present section.</Paragraph> <Paragraph position="3"> First let us take a look at the kind of tree we can construct from a given grid. We give the CLG in (11) as an example: (11) LTOP, G * be? null /,From this grid we can derive a superline 8PSa with {~G = {<a,b>,<c,d>,<e,f>,<e,a>,< e, c >}. If we interpret this as a dominance relation and if we draw dominance in the usual way, with the dominating element above the dominated one, we get the following tree: (12) e b d f This tree looks rather different than the structures used in the syntactic literature or in metricM work like \[Hayes, 1981\]. Yet there is one type of structure known in the linguistic (phonological) literature which graphically strongly resembles (12). These are the Defendency Graphs (DGs) of Dependency Phonology (\[Durand, 1986\] a.o.).</Paragraph> <Paragraph position="4"> According to \[Anderson and Durand, 1986\], DGs have the following structure. They consist of a set of primitive objects together with two relations, dependency and precedence. For example within the syllable/set/the following relations are holding (notice some of the symbols we introduced above are used here with a slightly different interpretation): Dependency s ,--- e --* t (i.e. /s/ depends on/e/ and/t/depends on ~el.</Paragraph> <Paragraph position="5"> Precedence s < e < t (i.e. /s/ bears a relation of 'immediate strict precedence to/e/which, in turn, bears the same relation to/t/.</Paragraph> <Paragraph position="6"> Anderson and Durand also introduce the transitive closure of 'immediate strict precedence', 'strict precedence', for which they use the symbol << and the transitive closure of dependency, 'subordination', for which they use the double-headed arrow. Moreover, well-formed dependency graphs conform to the 1. There is a unique vertex or root 2. All other vertices are subordinate to the root 3. All other vertices terminate only one arc 4. No element can be the head of two different constructions null 5. No tangling of arcs or association lines is allowed null 20.1 and 20.2 together form a redefinition of the Single Root Condition. Theorem 2 states that superlines of CLGs with the government requirement satisfy this Condition.</Paragraph> <Paragraph position="7"> Because 'arcs' are used as graphic representations for dependency (which is intransitive), 20.3 seems a formulation of the Single Mother Condition. Theorem 3 states that this condition also holds for superlines of complete linguistic grids.</Paragraph> <Paragraph position="8"> 20.4 needs some further discussion because it is the only requirement that does not seem to hold for our grids. The condition says that something cannot be a head at more than one level of representation, e.g. something cannot be the head of a foot and of a word. However, because of the CCC, in bracketed grid systems the head of a word always is present (as a star - hence as a head) on the foot level.</Paragraph> <Paragraph position="9"> It is exactly this requirement that is abandoned by all authors of at least Dependency Phonology. \[Anderson and Durand, 1986\] (p.14) state that one element can be the head of different constructions, as indeed we have already argued in presenting a given syllabic as suecesively the head of a syllable, a foot and a tone group.</Paragraph> <Paragraph position="10"> In order to represent this, a new type of relation is introduced in their system, subjunction. A node a is subjoined to/3 iff (~ is dependent on/3 but there is no precedence relation between the two.</Paragraph> <Paragraph position="11"> The word intercede then gets the following representation: null</Paragraph> <Paragraph position="13"> in ter cede We once again cite \[Anderson and Durand, 1986\] (p.15): The node of dependency degree 0 is ungoverned (the group head). On the next level down, at dependency degree 1, we have two nodes governed by the DDO node representing respectively the first foot (inter) and the second foot (cede). The first node is adjoined to the DDO node, the second one is subjoined. Finally, on the bottom level, at DD2, the nodes represent the three syllables of which this word is comprised. These latter nodes are in turn governed by the nodes at DD1 and once again related to them by either adjunction or snbjunction.</Paragraph> <Paragraph position="14"> Lifting the restriction this way seems to be exactly what is needed to fit the superline into the DG formalism. null 20.5 holds trivially in the bracketed grid framework as well. It can be interpreted as: if ~ precedes /3 on a given line in the grid, there is no other line such that/3 precedes c~ on that line. This is included in the definition of the '~' relation, The difference between a phonological DG and a bracketed grid is the same as the difference between a superline and a bracketed grid: the DG is not formally divided into separate lines. Interestingly, \[Ewen, 1986\] analyses English stress shift, one of the main empirical motivations behind the grid formalism, with subjunction. In \[Van Oostendorp, 1992b\] I argue that using subjunction Ewen's way actually means an introduction of lines into Dependency Phonology.</Paragraph> </Section> <Section position="5" start_page="327" end_page="329" type="metho"> <SectionTitle> 5 Government Phonology </SectionTitle> <Paragraph position="0"> Now let us turn over to a well-known phonological theory that also employs the notion of government as well as 'autosegmental representations'. I refer of course to the syllable theory of KLV and \[Charette, 1991\].</Paragraph> <Paragraph position="1"> This theory of the syllable in fact does not have a syllable constituent at all. In stead of such a constituent, KLV postulate a line of x-slots and paralelly, a tier of representation which conforms to the pattern (0 R)* - that is an arbitrary number of repetitions of the pattern OR.(KLV \[1990\]) The term 'tier' suggests an autosegmental rather than a metrical (bracketed grid) approach to syllable structure, but KLV are never explicit on this point.</Paragraph> <Paragraph position="2"> The fact that O and R appear in a strictly regular pattern can be explained either by invoking the (metrical) Perfect Grid requirement or, alternatively, the (autosegmental) OCP. The same applies to the 'labels' O and R: we can define them autosegmentally as the two values of a type 'syllabic constituent' or indirectly as notational conventions for stars and dots on a 'syllable line', i.e. we could have the following representations for KLV's (O R)* line: (14) a. tier:.</Paragraph> <Paragraph position="3"> \[type: syll.const; vMue: O;...\] \[type: syll. coast; v~lue: R;... \], etc.</Paragraph> <Paragraph position="4"> b. line: *, etc.</Paragraph> <Paragraph position="5"> For (14b), we would have to show that the rhymes or nuclei project to some higher line. We will return to this below.</Paragraph> <Paragraph position="6"> We still cannot really decide between an autosegmental and a metrical approach. If we look at more than one single line, this situation changes.</Paragraph> <Paragraph position="7"> At first sight, it then seems very clear that KLV's syllables act as ARs, not as grids. For instance, we can have representations like (15) (from \[Charette, 1991\]), with a floating Onset constituent:</Paragraph> <Paragraph position="9"> This is a possible autosegmental chart, but not a possible grid (because the Complex Column Constraint is violated by the word initial onset). However, empirical motivation for (15) is hard to find. As far as I know, the structure of (15) is motivated only by the assumption that on the syllabic line we should find (OR)* sequences rather than, say, (R)(OR)*.</Paragraph> <Paragraph position="10"> The same state of poor motivation does not hold, however, to the representation \[Charette, 1991\] assigns to words with an 'h aspir6'7:</Paragraph> <Paragraph position="12"> As is well known, the two types of words behave very differently, for example with regard to the definite article. While words with a lexical representation as in (16) behave like words starting with a 'real', overt, onset, words with a representation like (15) behave markedly different: (17) a. le tapis- *l' tapis b. la hache - *l' hache c. *la amie - l' amie It seems that, while the empty onset of (15) is invisible for all phonological processes, the same is not true for the empty onset of (16).</Paragraph> <Paragraph position="13"> rI disregard the (irrelevant) syllabic status of the final \[SS\] consonant.</Paragraph> <Paragraph position="14"> So there are two different 'empty onsets' in KLV's theory s. Notice that the type of empty onset for which there is some empirical evidence is exactly the one where the (0 R) - x slot chart does behave like a grid (i.e. where it does not violate the CCC). So whereas we have here a formal difference between KLV's theory and grid theory, this has no real empirical repercussions.</Paragraph> <Paragraph position="15"> Another similarity is of course the notion 'government'. For KLV, government only plays a role on the line of x-slots. \[Charette, 1991J(p. 27) gives the following summary: Governing relations must have the following properties: null (i) Constituent government: the head is initial and government is strictly local.</Paragraph> <Paragraph position="16"> (it) Interconstituent government: the head is final and government is strictly local.</Paragraph> <Paragraph position="17"> Government is subject to the following properties: (i) Only the head of a constituent may govern. (il) Only the nuclear head may govern a constituent head.</Paragraph> <Paragraph position="18"> The most important government relation is constituent government: this is the relation that defines the phonological constituent. Moreover, the 'principles' given by Charette are only introduced into the theory to constrain interconstituent government. By definition, constituent government remains unaffected by these. (As for (i), the definition of the notion constituent implies that it is only the head that governs and (it) does not apply because we never find two constituent heads within one constituent).</Paragraph> <Paragraph position="19"> The two conditions on constituent government (that the head be initial and the governee adjacent to it) can be expressed in our formalisation of the grid in a very simple way: Definition 21 Rx-stot =~'-&quot; According to KLV, *-- is the only possible constituent government relation. Other candidates like {---~, ~-,-~,,~} are explicitly rejected, so in fact we have (with some redundancy): Definition 22 VLi : \[R/E {~-)\] A R~-,lot =*'-8\[Piggot and Singh, 1985\] propose a different distinction, namely one in which the empty onset of ami is represented as (in) and the one of hache as (ib) (0 is a null segment):</Paragraph> <Paragraph position="21"> Under this interpretation of Government Phonology, the syllable structure is formally even more similar to grids, if we assume that the linking between segmental material and x-slots has to be outside the grid (treated as autosegmental association) anyway.</Paragraph> <Paragraph position="22"> This is one of the reasons why KLV do not accept the syllable as a constituent: under their definition of government, this would make the onset into the head of the syllabic constituent.</Paragraph> <Paragraph position="23"> At least we can see from these definitions that the x-slot line in KLV's theory behaves like a normal metrical line.</Paragraph> <Paragraph position="24"> Yet there is one extra condition defined on this line; this is called interconstituent government. Because of the restrictions in (15), KLV notice that this type of government only concerns the following contexts. (Square brackets denote domains for interconstituent government, normal brackets for constituent But the fact that there is an extra condition on a line does not alter its being metrical, even if we call this extra condition a government relation 9.</Paragraph> <Paragraph position="25"> We now have reached the following representation (20) of the grid variant of the x line in (19) (we use the star-and-dot notation and leave out the association of the autosegmental material to the skeleton):</Paragraph> <Paragraph position="27"> By definition, stars are present on a higher line.</Paragraph> <Paragraph position="28"> As we have seen above, there is no reason not to consider the (O R)* tier to be this higher line. We then get the following representation:</Paragraph> <Paragraph position="30"> p a t r i As we noted above, KLV do not accept any constituents on the higher line. One of their reasons was their stipulation that all constituents are left-headed. There are independent reasons to abandon this restriction. \[Charette, 1991\] argues for a prosodic analysis of French schwa/\[e\] alternations. In order to do this, she has to build metrical (Is w\] labeled) trees representing feet on top of the nuclei. She gives the 9In \[Van Oostendorp, 1992a\] I sketch a way of translating 'interconstituent government' to a bracketed grid theory of the syllable.</Paragraph> <Paragraph position="31"> following crucial example \[Charette, 1991\] (p.180, ex-</Paragraph> <Paragraph position="33"> Here we have a clear case of a right-headed phonological constituent, namely the foot.</Paragraph> <Paragraph position="34"> Furthermore, we see that the nuclei are projected from the (O R)* line to aiine where they are the single elements. If we change the top N's in this picture into ~'s we have something like a metrical syllable line.</Paragraph> <Paragraph position="35"> If we incorporate these two innovations into our theory, we can translate th structure in 22 into a perfectly normal grid, in fact into a complete linguistic grid:</Paragraph> <Paragraph position="37"> Concludingly, we can say that, although KLV's syllable representations are somewhat different from linguistic grids, two minor adjustments can make them isomorphic: * in stead of (O R)* we assume (R)(O R)*, i.e. there can be onsetless syllables (KLV themselves note that most of the (O R)* stipulation can be made to follow from independent stipulations like interconstituent government). This follows a forteriori for the (R)(O R)* stipulation.</Paragraph> <Paragraph position="38"> * in stead of 22 we assume VR~ : \[R~ E {~--, }\] ^ R~_,~. =*--The first conjunct of this definition is simply my translation of Kager's (\[1989\]) Binary Constituency Hypothesis 12 and the second conjunct does the same as the original definition of KLV: it gives the correct choice of government for the subsyllabic line.</Paragraph> <Paragraph position="39"> As far as I can see, none of these modifications alters the empirical scope of KLV's theory in any important way. I conclude that for all practical purposes, KLV's representation of the syllable equals my definition of a linguistic grid.</Paragraph> </Section> class="xml-element"></Paper>