02ne,   PDF
Mark Newson

The coordination particle

1 Introduction This paper continues previous work by Newson & Gaspar (2001a, 2001b, 2002|henceforth Newson & Gaspar), which deals with ellipsis in coordinate expressions. The focus of the present paper is not however on ellipsis, but on questions concerning the form of coordination, elided or not, with particular emphasis on the distribution of the coordination particle (and, or, but etc.) across languages. In the following section I will brie y introduce the framework I will adopt (essentially that of Newson & Gaspar). I will then proceed to the analysis. The section on the analysis is divided into four subsections which concern my claims about the nature of the coordination particle, a review of the linguistic variation concerning this element, the actual analysis in terms of alignment constraints and nally a brief look at languages which do not always represent the coordination particle overtly.

2 The framework The framework that I adopt is a very restrictive version of OT, though it incorporates many standard features. The restriction lies mainly in the evaluation, in that it is assumed that this consists only of alignment and faithfulness constraints. As is standard, I assume that the input consists of a set of lexical selections plus a number of feature assignments. These feature assignments concern tokens taken from the argument structure of the predicates included in the input (thematic roles), markers of grammatical function (i.e., subject) and markers of information status (topic and focus). 1 Thematic and information features are assigned randomly to arguments and determine how these arguments are to be interpreted: a di erent feature assignment constitutes a di erent input. The grammatical function feature, however, is 1

In the inputs presented below, the thematic features are represented as x and y, where x denotes a more prominent thematic role than y, and the subject feature is given as sub. Examples including information features are not considered in this paper.

T H E E V E N Y E A R B O O K 5 (2002) 95–116

ISSN 1218–8808

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assigned to the argument which is assigned the most prominent thematic feature of a predicate, where prominence is determined in terms of a universal thematic hierarchy (for some discussion of argument prominence, see Grimshaw 19902 ). Assuming that it is the input and not the generated expression that feeds the semantic interpretation, the question of the \correctness“ of feature assignments, as well as that of the lexical selection, reduce to conditions on interpretability. It is only interpretable inputs that we need be concerned with. The question of which expressions compete for grammaticality is much simpli ed under the restrictive assumptions I will be making. I assume that gen is a simple linearisation procedure which produces all the possible linear orderings of the input elements. Moreover, any assigned feature may be the target of underparsing and thus candidate expressions will also di er in terms of which input features are present or absent. Notice that under these assumptions the candidate set is nite. The evaluation component of the grammar contains constraints which are violable and ranked in accordance with the normal OT view. However, as mentioned above, I will assume that this part of the grammar contains only alignment and faithfulness constraints. The alignment constraints are gradient constraints, violable to di erent degrees, which favour candidate expressions in which certain elements are adjacent to (aligned with) each other. Typically alignments concern feature bearing elements (e.g., subjects, topics, etc.) which are aligned with respect to a \core” element: the head. In this paper I will assume that the predicate is the head of the clause. For every alignment pair (subject/predicate, topic/predicate etc.) there is a left and a right alignment, the ranking of which with respect to each other and with respect to the other constraints will determine on which side of the head an aligned element will come and how near to the head it will be. Note the indication here that there are two ways to violate an alignment constraint: (i) the aligned element may be on the wrong side of the head, something we will refer to as a side violation and represent in tables with \★“; (ii) the aligned element may be on the right side of the head, but not 2

Grimshaw determines the notion of argument prominence in terms of two hierarchies, a thematic one (agent > experiencer > obliques > theme) and an aspectual one (arguments associated with prior events > arguments associated with resulting events/states). For Grimshaw, the notion of external argument is defined as the argument which is most prominent on both hierarchies. If there is conflict between the two, then the notion remains undefined for that predicate. However, following Newson (1999), I will assume that for the assignment of the sub feature conflicts are resolved by giving the aspectual hierarchy priority over the thematic one.

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adjacent to it, which we will refer to as an edge violation and mark with the standard \”. The important assumption is that one side violation is worse than any amount of edge violations. Under these assumptions the grammar has no cause to refer to structure; it simply considers which elements are aligned to which others in a linearly organised expression (Newson 2000). Structure, if it has any reality in syntax, is epiphenominal. The one faithfulness constraint I will assume in this paper is parse: a constraint against underparsing. Filling syntactic positions with non-input elements is not part of the present system. This has the e ect of both restricting the types of constraints made use of as well as maintaining a nite candidate set. If candidates expressions are allowed to di er through the insertion of non-input material, then obviously the candidate set would be potentially in nitely large. As underparsing has a limit, i.e., the null candidate, this process can only increase the candidate set nitely. 3 Newson & Gaspar take coordination to be marked in an input by the presence of a coordinator which is \predicate“-like, determining a number of \argument” slots to which it assigns coordination features. An input involving a coordination may therefore look like the following: (1) & x =arrived x =sub=John y =fainted x =sub=Mary 3

There may be a way to include a very limited amount of insertion of non-input material under the assumption of a “split-lexicon” in the manner of the Distributed Morphology model (Hale & Maranz 1993). From this perspective what is in the input is a set of abstract lexical elements, consisting of bundles of syntactic and semantic features, which may or may not correspond to any particular phonological word of the language. Once the optimal arrangement of these abstract lexical elements is determined, then the expression can be “spelled out” with words from the phonological lexicon on a “best fit” basis. Suppose that the best fitting phonological word for spelling out a certain abstract lexical element is one which is associated with more features than the element to be spelled out. For example, it may be that the phonological word do happens to be the best way to spell out an abstract verb which has grammatical but no semantic features, borrowing an idea from Grimshaw (1997). In this case there would appear to be non-input material inserted into an expression though this would obviously be limited by the choice of phonological words in the lexicon.

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Note that it is assumed that what is marked as coordinated in the input are predicates, not phrases or clauses. This must be so as such elements do not exist in the input.4 A non-standard feature of the evaluation in the present system is that it is cyclical. Standardly it is assumed that the entire candidate set is evaluated on a single run through the ranked constraints, each (surviving) candidate being evaluated against others in terms of its sum performance with respect to each constraint in turn. Each constraint imposes limitations on the surviving candidates until the candidate set is reduced to the optimal one(s). The idea of cyclicity is that candidate expressions can be evaluated not in their entirety but more selectively, concentrating on speci c aspects of their organisation; a di erent aspect for each cycle. On each cycle the candidate set is decreased and the surviving candidates form the starting set for evaluation on the next cycle. What cyclicity does is to prioritise the satisfaction of constraint conditions for certain aspects of candidate expressions. For example, if we assume that the requirements of superordinate predicates are attended to in the rst cycle and the successively subordinated predicates in subsequent cycles, then constraint conditions may be satis ed for superordinate predicates at the expense of forcing subordinate predicates to violate them. A subject may be raised to satisfy the requirements of a higher predicate at the expense of forcing the lower one to violate exactly the same condition. The candidates which survive a cycle will all be similar in that they are optimally arranged with respect to whatever was the focus of that cycle and any previous ones. However, they will di er precisely in terms of those aspects not yet considered. Given that on each cycle candidates are eliminated, it follows that the later cycles will have fewer opportunities to satisfy the constraint requirements, but as is standard in OT, the best satisfaction of these conditions, given prior limitations, will be grammatical. In Newson & Gaspar, this idea was utilised to give an analysis of ellipsis in coordinate structures. Two cycles are assumed: the predicate cycle and the coordination cycle. In the predicate cycle, the requirements of speci c arguments and predicates thematically related in the input are 4

The semantics may interpret such an input as representing a coordination of propositions, taking the predicate to be the semantic head of the proposition, not at all an unusual assumption. As we will see, in the syntax, as no structure is assumed and hence there are no phrases or clauses, it is predicates which are coordinated, in the sense that these are ordered with respect to each other by the coordination alignment constraints.

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attended to. Thus in this cycle related arguments and predicates will be sorted into their alignment positions. When coordination is involved, the relationship between coordinated predicates will not be attended to in the predicate cycle as this relation is not thematic. Thus in e ect each of the conjuncts will be evaluated in this cycle as though they are independent of each other and the result will be that only candidates in which the relevant arguments are properly aligned to their predicates in each conjunct will emerge from this cycle. However, the order of the conjuncts themselves will not be xed and neither will the position of the coordination particle. Therefore candidates surviving this cycle will di er exactly in these respects. It is up to the coordination cycle to determine which of these candidates is optimally organised. To give a simple example, I introduce two alignments here: one which aligns the subject to the right or left of its predicate (Sp/pS) and one which aligns arguments to the right or left of the predicate (Ap/pA). For English given that the subject precedes and other arguments follow the predicate, the ranking of the constraints is as in (2): 5 (2) Sp > pA > pS , Ap Now consider a simple input involving coordination, such as in (1). Ignoring the issue of the coordination particle for the moment, as there are four input elements, there will be 12 possible orderings of these, which constitute the candidate set.6 In the predicate cycle the speci c thematic relationships stated in the input are attended to and each subject is forced in front of its predicate. However, the predicates themselves will be unordered with respect to each other:7 5

For this simplified demonstration the ranking of the pS and Ap constraints is unimportant. This does not mean to say that it would be unimportant if we were to consider further phenomena.

6

As it is not relevant for English, we also ignore here the possibility of feature underparsing.

7

In the following table for convenience I have represented non-optimal candidates in terms of their types, i.e., whether subjects are separated from their predicates by other input material or the subject is on the wrong side of its predicate (e.g., John Mary fainted arrived or John arrived, fainted Mary). The three dots in candidate expressions represent the possible positions of the other input material. The dots in the columns under the constraints represent different degrees of violation depending on the exact arrangement of the other input elements in the candidate.

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predicate cycle

R John arrived, Mary fainted R Mary fainted, John arrived John arrived :::

:::

:::

arrived John : : : : : : Mary : : : fainted : : : : : : fainted Mary : : : :::

Sp

pA

: : : !

★★ ★★ ★★ ★★ ★: : : ★: : :

★: : : !

pS

: : :

:::

:::

★: : :

:::

:::

★: : :

 : : : ! ★: : : ★: : :

★: : : !

Ap

: : :

As can be seen, what emerges from this cycle are the two candidates in which the two conjuncts are individually properly organised, but unordered with respect to each other. In this particular case, the coordination cycle will not select between these two candidates either and so both will emerge as optimal and therefore grammatical. The assumption is that coordination is a symmetrical relationship and thus under normal circumstances there can be no way to x the order of conjuncts. Therefore, all else being equal, the order of the conjuncts will remain un xed8 (in elliptical cases all else is not equal and hence an order on the conjuncts will be imposed | see Newson & Gaspar for details). The relationship between the coordination particle and the conjuncts is also not thematic and hence this will not be dealt with in the predicate cycle. Given that we start with a candidate set consisting of all the possible linear arrangements of the input elements (and all possible under parsing of their features) and that the predicate cycle will x the order of elements within the conjuncts, entering the coordination cycle will be those candidates in which the coordination particle appears in all possible juxtapositions with respect to the conjuncts. In the coordination cycle, therefore, the order of the coordination particle with respect to the conjuncts must be xed. We now turn to the issue of how this can be done.

8

We take a fairly standard view on sequencing effects seen in certain cases of coordination, as in John drank the poison and John died, for example, claiming this to be pragmatic in nature, lying outside the scope of our considerations.

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3 The analysis 3.1 The nature of the coordination particle

The most obvious treatment of the coordination particle is to take it as representing the input coordination element itself. Two observations argue in favour of this. First, the particle is used to distinguish di erent types of coordination: (4) a. John arrived and Mary fainted b. stop or I’ll shoot c. John fetched the drinks but Mary paid for them Given that these di erences are marked on the coordination element in the input, it would be straightforward to assume that the particle is simply an instantiation of this element. Secondly, as Borsley (1994) points out, the coordination particle has certain \head“-like properties. This ts well with our treatment of the coordination elements as an \argument” taking head in the input. One \head“ property that the coordination particle has is that it tends to conform to the general head sidedness conditions of the language. Thus, if the language is basically head initial, the coordination particle can be analysed as being initial, in that it appears to be more closely associated with the conjunct that follows it, whereas in head nal languages the particle is probably better analysed as being closely associated with the preceding conjunct. Thus, in English we can strand a coordination particle with a following conjunct, but not a preceding one and in Japanese in cases of multiple coordination marking, the particle obviously follows each conjunct: (5) a. John is coming, and Mary/*Mary and b. taroo to akiko to wa nara e ikimashita Taro and Akiko and top Nara to went `both Taro and Akiko went to Nara’

(Borsley 1994 : 224)

However, there are other reasons why it might not be wise to assume that coordination particles instantiate the input coordination element. One comes from observations such as (5b). Here, in the same coordination the particle appears more than once. Clearly there is only one coordination here as there are only two conjuncts. Neither is this unusual phenomena, as it can be found in a number of geographically and historically disperse languages:

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(6) a. i Jan i Jerzy widzieli Mari¦ and Jan and Jerzy saw-m.pl Maria-acc. `both John and Jerzy saw Mary’ (Polish, Borsley 1994 : 241) b. ke egho ke o petros to thelume and I and the petros it want-1pl `both Peter and I want it’ (Greek, Johannessen 1998 : 91) c. et ego et Cicero meus agitabit and I and Cicero my will-demand-3sg `both I and my Cicero will demand (it)' (Latin, Johannessen 1998 : 91) d. et Jean et Marie sont alles au parc and Jean and Marie were-3pl gone to the park `both John and Mary have gone to the park’ (French, Gaspar 1999 : 2) Even if these constructions are special in some way, in that they are used to intensify one or both of the conjuncts, as their English translation suggests, it would be clearly dicult to relate both appearances of the particle to a single input element. Instead, it seems the particle is to be seen more as part of the individual conjuncts, rather than as an independent element linking them. Further evidence to this e ect is the fact that often the form of the coordination particle is dependent on properties of the conjuncts themselves. Johannessen (1998) reports that Nguan, a Melanesian language from the Central New Hebrides, coordinates VPs with poo and clauses with go : (7) a. A ga vano poo tape na-peka seara I non-past go and get yam some `I go and get some yams’ b. eu munu na-maloku go eu sale poogi they drink kava and they dance all night `they drank kava and they danced all night’ (Johannessen 1998 : 86) Similarly Sissala, a Voltaic language, has a di erent coordination particle for sentence (ka ), VP (a ) and all other coordinations (r):

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(8) betuu coNgoroN per mEtrE bEllE ka u zN ma peri elephant height reach meters two and his weight also reach klo bui-ammuO kilos thousand- ve `the elephant’s height reaches two meters and his weight can also reach ve thousand kilos’ (9) I sisnyE siE tOk niN a mu a coki yibuu na a nyikE you now so take re and go and cut mound def and light a ba yila viva and cut mound walk `you clear the mound place there and burn (the place). You now form the mounds while walking’ (10) pilEkE r wOw
ulEnErE nE muE he baksE chameleon and spider went put farms `the chameleon and the spider went and made their farms’ (Johannessen 1998 : 85) From the present perspective it cannot be the category of the coordinated elements which are responsible for these di erences as, at least for VP and clausal coordination, we assume that there are no categorial di erences: both are cases of predicate coordination. However, there are di erences in terms of ellipsis, which is what I assume is being marked here. A similar but more transparent case of this comes from Pitjantjatjara, an Australian language of the Western Desert Group, which encodes the referential properties of the subjects of coordinated clauses in the coordination particle: panya kunkunpa ngari- ngi (11) ka kunyu kuta and-ds rep older brother anaph sleep lie-past imp ka kunyu tjitji panya paluru ngalya-pitja-ra ngari-kati-ngu and-ds rep child anaph he back-come-ant lie-bring-past munu kunyu ngari- ngi kunkunpa and-ss rep lie-past imp sleep `The elder brother was lying asleep and the child came back, lay down and (the child) was asleep’ (Bowe 1990 : 96) Of interest to us from this rather long example taken from a narrative is the use of the coordination particles ka and munu. The rst is used when the following clause has a subject di erent to the previous one, as can be

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seen overtly in the rst two conjuncts ( kuta and tjitji respectively). The conjunction munu is used when coordinated clauses have the same subjects, as can be seen in the last sequence of conjuncts. Here the subject of `lay down’ and `was asleep’ is covert, but its reference is the same as the subject of `came back’ because they are conjoined with munu. Thus in this case not only does the conjunction particle mark null material in the conjuncts, it also represents properties of the null material itself. Whatever the analysis of these phenomena, the point remains that it is properties of the conjunctions that determine the form of the particle, which would be rather dicult to account for if we assumed that the particle is an instantiation of the independent coordination element. The above properties are more easily captured if we take the coordination particle to simply be a marker of the coordinated status of the conjuncts, in a similar way to how a complementiser is a marker of the subordinated status of the clause it introduces. More accurately, given that we are assuming that it is predicates which are marked as coordinated in the input, I will take the coordination particle to be a marker of the coordination feature assigned to the predicate. In general, features assigned to an element in the input, if represented morphologically at all, can either be realised in terms of a bound or a free morpheme. For example, a negative feature can in English be realised as a free not or a bound n’t. The subject feature assigned in the input to the most prominent argument can be realised in terms of an in ectional (case) morpheme, however, in some languages, notably Bantu, there is an obligatory pronoun which can be taken to be the realisation of the subject feature by a free morpheme. There are many cases of elements being represented morphologically in one language but by an independent word in another, for example much of what goes under the title of incorporation can be analysed along these lines. Obviously then this is a rather general \parameter” of variation between languages. I will assume, though not fully develop an account of the phenomena, that this variation has to do with how the feature gets instantiated in a candidate expression: \fused“ with the element to which it is assigned or independent from it.9 In the cases we are concerned with, the coordination particle is an independent realisation of the coordination feature assigned to a predicate. Of course, it has to conform to alignment conditions with respect 9

Clearly, given the restriction to alignment constraints, the difference between the two cases has to do with whether the feature is morphologically or syntactically aligned. The difference is between whether or not the alignment condition sees elements internal to the lexical word.

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to the predicate to which it is assigned. We will consider these alignment conditions after the following section. 3.2 Linguistic variation and the coordination particle

Cross-linguistically, we nd the following variation concerning the positioning of the coordination particle: (12) a. the coordination particle comes to the right or the left of the conjunct (predicate) which it marks; b. the coordination particle marks all or only one of the conjuncts c. the coordination particle, if it does not mark all of the conjuncts, marks the right-most or the left-most conjunct. We have already exempli ed the variation mentioned in (12a) referring to the di erence between English and Japanese (see (4) and (5)). There we gave examples of nominal coordination, which will not concern us much in the rest of this paper. However, the same distinction seems to hold of \clausal” coordination too: (13) John wa biru ga kirai de, Mary wa sukida John top beer obj hates and Mary top loves `John hates and Mary loves beer’

(Newson & Gaspar)

That the coordination particle is attached to the rst conjunct in the Japanese example is attested by the intonation pattern, which, as indicated by the comma, pauses after the particle. With clausal coordination in English, however, the pause tends to precede the coordination particle: (14) John arrived, and Mary fainted We have also seen examples of the second axis of variation when we showed that in some languages coordination can be marked on both conjuncts (see (6)). Other languages do not allow this possibility, for example English:

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(15) *and John arrived and Mary fainted10 Of course, it is possible to have multiple instances of coordination particles in English sentences: (16) John arrived and Mary fainted and Bill applauded However, as Borsley (1994) points out such sentences have a very different organisation to those with just a single coordination particle. In a language like English, multiple coordination particles mean multiple coordinations. This can be demonstrated by the following contrast: (17) a. John wrote the letter, Mary posted it and Bill received it on Tuesday b. John wrote the letter and Mary posted it and Bill received it on Tuesday Note that (17a) is two ways ambiguous, with the adverbial on Tuesday either modifying all of the conjuncts, or just the last. Importantly, we cannot interpret this to mean that John wrote the letter, say, on Monday and that Mary posted it and Bill received it on Tuesday. However, this is a possible interpretation for (17b). Thus, only in (17b) can the last two conjuncts be interpreted as a semantic unit able to be modi ed as such. Similarly, consider the following: (18) a. John wrote the letter, Mary posted it on Tuesday and Bill received it (on Wednesday) b. John wrote the letter and Mary posted it on Tuesday and Bill received it (on Wednesday)

10

The examples of multiply marked coordination given in (6) all concern nominal coordination. I have not been able to confirm whether any of these languages allow multiply marked sentential coordination. If such reiteration of the coordination particle has the function of intensifying one or both of the conjuncts, then the fact that we can get examples such as (i) and (ii) which have the same intensifying effect suggests that multiply marked sentential coordination should at least be a possibility: (i) either you have the money or you don’t have it (ii) both that John had seen Mary and that he had spoken to her were worrying

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In (18a) the adverbial can only modify the immediately preceding conjunct and not the two preceding conjuncts together. This interpretation is however possible in (18b). What this indicates is that there are multiple coordinations in the (b) examples which give rise to an ambiguity in semantic structure. From the present perspective, this di erence can be traced back to the organisation of the input. The (a) examples have an input of the pattern given in (19) in which there is one coordination, with multiple \arguments“. The (b) examples have inputs of either of the patterns shown in (20) or (21), where coordinations are embedded. (19) & x = wrote :::

y = posted :::

z = received :::

(20) & x = wrote :::

y=& x = posted :::

(21) & x=& y = wrote :::

x = posted :::

y = received

y = received

:::

:::

The conclusion is, therefore, that English only allows multiple coordination particles if there are multiple coordinations, with one particle marking one coordination.11 The nal axis of variation, mentioned in (12c), has again already been exempli ed. Compare the Japanese and English examples in (13) and (14) once more. (13) John wa biru ga kirai de, Mary wa sukida John top beer obj hates and Mary top loves `John hates and Mary loves beer’ (14) John arrived, and Mary fainted In Japanese, the coordination marked conjunct precedes the one which is unmarked, whereas in English it is the unmarked one which precedes the marked one: 11

This situation is very similar to that which holds in negative contexts where languages either have multiple marking of a single negation, known as negative concord, or a single marking for every negation, known as double negation. See Newson 1998.

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(22) a. *John wa biru ga kirai Mary wa sukida de b. *and John arrived Mary fainted 3.3 Candidates and alignments

Let us take a hypothetical example concerning a coordination of two predicates heading propositions which we will denote P and Q. Assuming there to be no ellipsis in these, emerging from the predicate cycle will be those candidate expressions in which P and Q are each individually well formed sentences, but arranged in any order with respect to each other, as shown in (3). Moreover on the assumption that the predicate cycle does not consider the issue of the realisation of the coordinate feature assigned to each predicate, this will also remain un xed. The possibilities are that neither, one or both features are marked and if they are marked the particle can be either to the left or the right of the marked conjunct. Bearing in mind that we are concerned with linearly arranged expressions, this gives 20 candidates entering the coordination cycle: (23) a. P Q b. & P Q c. P & Q d. P Q & e. & & P Q f. & P & Q g. & P Q & h. P & & Q i. P & Q & j. P Q & &

k. Q P l. & Q P m. Q & P n. Q P & o. & & Q P p. & Q & P q. & Q P & r. Q & & P s. Q & P & t. Q P & &

Clearly the majority of these are ambiguous in terms of which conjunct is being marked by which particle. However, this ambiguity is not a problem for the evaluation of the candidates as each candidate will be evaluated in terms of its best satisfaction of the constraints. This follows from the fact that not only will the suboptimal analyses of the candidates never be optimal as they are harmonically bound by the optimal analyses, they will also never play a role in determining the optimal candidate by eliminating

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an otherwise even more optimal candidate, for example.12 The suboptimal analyses of these candidates can therefore be safely ignored. What the best satisfaction of the constraints is will obviously depend on the ranking of the constraints. Under di erent rankings, di erent analyses of certain candidates may be relevant. Given the range of variation amongst languages shown in (12) we need a system which will select candidates in terms of: which side of the conjunct the coordination particle comes; whether all or just one conjunction is marked by a particle and the order of the conjuncts when one is marked but not the other. The rst of these is probably the most straightforward as it simply requires constraints which favour the coordination particle on the left or the right of its relevant conjunct. There is nothing particularly special about such an alignment: (24) &p/p&: a coordination feature assigned to a predicate is to the left/ right of the predicate Given that this constraint operates in the coordination cycle, after the predicate cycle, the nearest to the left or the right that the particle can be placed to its predicate is in front of or behind the \clause” headed by the predicate. The next axis of variation concerns whether the coordination feature is realised or not on all conjuncts. Given that the case where the feature is not realised involves the underparsing of the feature, it is clear that the faithfulness constraint must be relevant here. However, this cannot be the whole story. Combining the faithfulness constraint with the two particle constraints in (24), we get six possible rankings giving rise to just three distinct language types, as three of the rankings produce the same result as some other ranking. The three language types are:

12

The demonstration of this is simple enough. Suppose con is the highest ranked constraint which differentiates between two candidates Canop and Cansub . The suboptimal candidate Cansub cannot do better against any other candidate than Canop with respect to any constraint ranked higher than con as by assumption con is the highest ranked constraint on which they are differentiated. Therefore any candidate which is beaten by Cansub with respect to a constraint higher ranked than con will also be beaten by Canop an hence Cansub has no effective role in determining the optimality of Canop .

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(23a/k) &p > p& > faith