1. Introduction

In this paper, we begin by introducing the comparison constructions in Yorùbá. Next, we investigate the distribution of norm-related readings in Yorùbá and review how this distribution has been predicted for English and Russian in the literature.

This paper is structured as follows: in the first section, we specify (i) what an exceed-type language is (1.1.), and (ii) what norm-relatedness is (1.2.). In the second section, we first introduce the main comparison constructions of Yorùbá (2.1.), since this has not yet been done in the literature. These data serve as the empirical basis for our research. Secondly, we show how these data could be analysed under a scalar approach (2.2.), and point out puzzles which we have not resolved yet. The last section is devoted to the distribution of norm-related readings. We first reflect on the main characteristics of the norm (3.1.). In (3.2.), we present and compare the distribution of norm-related readings in four languages (English, German, Russian, and Yorùbá). In (3.3.), we show how Rett 2008 and Krasikova 2009 predict this distribution and argue that normrelatedness is not a binary phenomenon, but a graded one.

1.1. Exceed-type languages

The exceed-strategy is one of the major strategies used by natural languages to express comparison (Stassen 1985). It has two main characteristics. First, two predicates are combined: a gradable predicate expresses the dimension along which the comparison is carried out, and a predicate meaning exceed conveys the ordering relation. Secondly, the standard of comparison – e.g. Isaac in (1) – functions as the direct object of the exceed-predicate.

In this paper, we investigate aspects of the comparison in Yorùbá (Benue-Congo, Defoid, Nigeria). It exemplifies the exceed-strategy as follows: the exceed-predicate ju, ‘exceed’, builds a serial verb construction with the gradable predicate – e.g. ga, ‘be tall’, in (1)¹.

(1) Adé ga      ju            Isaac    lọ²

Adé be.tall    exceed    Isaac    sm

‘Adé is taller than Isaac.’

In a sample of 167 languages, Stassen 2008 classifies 33 languages as exceed-type languages, i.e. languages which use the exceed-strategy to express comparison. Most of them (24) are located in sub-Saharan Africa. This type is distributed across language families. There are exceed-type languages within the Niger-Congo, the Afroasiatic, and the Nilo-Saharan phyla. Only the Khoisan phylum does not have any representative of this type.

1.2. Norm-relatedness

The positive construction in (2) – like its English counterpart – is norm-related³, since the characterization of its truth-conditions involves the reference to some contextually given norm. Intuitively, (2) is true in a situation if Nadjib – the compare – is taller than some standard size salient in the situation (but see Kennedy 2007a for additional details).

(2) Nadjib    ga

Nadjib          be.tall

‘Nadjib is tall.’

Before turning to the distribution of norm-related readings across comparison constructions in section (3), we explore – in section (2) – the main characteristics of these comparison constructions.

2. Yorùbá: an exceed-type language

2.1. Comparison constructions in Yorùbá: An overview

Apart from the data in Stassen 1985 and very scarce mention in the literature, the exceed-strategy has not yet enjoyed – to our knowledge – an in-depth study. We therefore present in this section the data in some detail before considering how these data could be covered in the scalar approach to the semantics of comparison constructions (developed in Cresswell 1976, von Stechow 1984, a.o.).

Syntactically, we assume that the gradable predicate and the exceed- predicate build a serial verb construction. The diagnostics used to detect such a construction are: (i) (aspectual, modal) auxiliaries can only appear once in such a sequence, and (ii) the direct object of the second predicate can be extracted (e.g. because of focalization) (Déchaine 1993). As shown in (3) and (4), auxiliaries cannot appear twice in a comparative construction⁴. (5) shows that extraction of the direct object is possible, whereas such an extraction is not possible in a coordination (6). (7) shows that the ungrammatical status of (6) can be imputed to the extraction of the direct object.

(3) *Max    ń                ga           ń            ju            Bob          lọ

Max            prog         be.tall    prog    exceed    Bob          sm

(4) *Max    lè               ga            lè          ju            Bob          lọ

(Max          can             be.tall     can       exceed   Bob         sm

((5) Bob                        ni            John     ga            ju             lọ

(Bob                              foc         John     be.tall     exceed    sm

‘It’s Bob that John is taller than.’

(6) *Bob    ni               John        ga,         ó             sì              ju             lọ

(Bob           foc            John       be.tall   he           and         exceed    SM

((7) John   ga,             ó               sì           ju            Bob         ọ

(John         be.tall       he             and       exceed   Bob         sm

‘John is tall and he exceeds Bob.’

The status and the exact distribution of lọ in comparison constructions remain unclear. lọ also means ‘go’ as in (8), where it functions as the main predicate of the clause. Nevertheless, we consider lọ in (1) and in (8) to be homonyms rather than one lexical item⁵. The absence of lọ slightly degrades the grammaticality of comparatives (9)⁶. In excessives (10), its presence renders the clause ungrammatical, whereas its distribution in superlatives matches its distribution in comparatives (11). We assume that it functions as a standard marker in comparatives as than does in English (Kennedy 2007b). Like than, lọ cannot be used in equatives, as shown in (12). It is furthermore interesting to note that cross-linguistically, the standard marker also often has a directional meaning (Kennedy 2007b).

(8) Màmá     lọ                  sọjà

Mother         went              to.market

‘The mother went to the market.’

(9) John        ga                 ju            Isaac            ^?(lọ)

John              be.tall          exceed    Isaac            (sm)

(10) Adé        ga                 ju             (*lọ)⁷

Adé                be.tall          exceed    (SM)

‘Adé is too tall.’

(11) Adé        ló                  ga              ju                ^?(lọ)

Adé               foc.he          be.tall      exceed         (sm)

‘Adé is the tallest.’

(12) ó            ga                  tó              mi                (*lọ)

He                be.tall            reach       me                (sm)

‘He is as tall as me.’

We now turn to other comparison constructions. As seen in (12), equatives use the predicate tó, ‘reach’, instead of ju. As for the comparative, the standard of comparison is in the accusative case. It is visible in (12), since Yorùbá morphologically marks case on pronouns. Apart from the two predicates ju and tó, there is no morphology specialized for comparison constructions. Excessives (10) and enough-constructions (13) make use of these two predicates, respectively.

(13) Adé    ga           tó          láti    ṣeré    nínú    ẹgbẹ    náà

Adé            be.tall    reach    to      play    in         team    the

‘Adé is tall enough to play in the team.’

The positive construction is morphologically the simplest one (see (2)). Ga is syntactically a verb. It is sometimes called a ‘quality verb’, since it denotes a quality⁸.

The superlative is a combination of comparative morphology and overt focus marking (see (11)). The superlative is, cross-linguistically, often marked by comparative morphology and additional features from the focus or definiteness marking system. In Romance languages, for example, the superlative is expressed by the interaction of comparative morphology with definiteness, as in French (14).

(14) Paul    est    le      plus      grand

Paul            is      the    more    tall

‘Paul is the tallest.’

A further type of modification is through reference to measurements for dimensions which are associated with a measurement system, e.g. height, cost, etc. This is illustrated with the measure phrase construction in (15) and the differential construction in (16). This reference can also be asked for as shown in the degree question in (17). We consider (17) to be a degree question, since (15) is an adequate answer to it. Degree questions can typically be answered by using a measure phrase construction.

(15) Kathy    ga           ní    ìwọn                  ẹsẹbàtà    márùn    àt’ààb^ọ

Kathy            be.tall    at    measure            foot           five          and’half

‘Kathy is 5.5 feet tall.’

(16) Naomi fi    ẹsẹbàtà    kan    ga            ju            Sandra     lọ

Naomi use        foot            one    be.tall    exceed    Sandra    sm

‘Naomi is 1 foot taller than Sandra.’

(17) Báwo  ló              ṣe        ga           tó?

How.qm    foc.she    how    be.tall    reach

‘How tall is she?’

In this section, we have introduced the main comparison constructions in Yorùbá. We now turn to a scalar analysis of these data.

2.2. Is a scalar analysis applicable to the Yorùbá data?

In this section, we consider what has to be assumed in order to apply the scalar approach developed for English (Cresswell 1976, von Stechow 1984, a.m.o) to the Yorùbá data. The basic axioms of the scalar approach – also called degree-based approach – are summarized in (18). It should be noted that each of these axioms has been challenged in the literature⁹, the result being that various versions of the scalar approach have emerged. We present a version of the scalar analysis which follows Beck (in print).

(a) (18) Measurement and comparison are formalized in terms of degrees,

(b) a degree is a point on a scale,

(c) a scale is a set of points totally ordered defined for some dimension (like height, cost, weight, intelligence, etc.),

(d) the semantic type ‹d› for degrees is added to the basic ontology, i.e. ‹e› for individuals, and ‹t› for truth values;

(e) gradable predicates have a degree argument in their lexical entry, as shown in (19).

(19) ||tall_{‹d‹e, t››}|| = λd_d. λx_e. Height (x) ≥ d; i.e. x is tall to degree d¹⁰.

In this approach, the English translation for (1) receives the logical form (LF) in (20) ¹¹. We follow the analysis of phrasal comparatives in Heim 1985 (for alternatives see Kennedy 1999, a.o.). The lexical entry for the comparative morpheme is given in (21) ¹².

(20)

(21) ||-er₁|| = λy.λg.λx. max {d|g(d)(x)} > max {d’|g(d’)(y)}

This approach derives the intuitively correct truth-conditions for the phrasal comparative:

(22) max{d|Height (Adé) ≥ d} > max{d’|Height (Isaac) ≥ d’}

‘max’ is a function which picks the maximal degree from a set. Application to the Yorùbá phrasal comparative is rather straightforward (see (23)). The syntax of the VP nodes follows Déchaine (1993: 803). The exceed-predicate is given the semantics of the English comparative morpheme (see (21)). As in English, an additional lexical entry like (24) is required for the comparative with degree (25).

(23)

(24) ||-er₂|| = λd.λg.λy. max{d’|g (d’)(y)} > d

(25) Kathy    ga    ju    ẹsẹbàtà    márùn    àt’ààbọ    lọ

Kathy    be.tall    exceed    foot    five    and’half    sm

‘Kathy is taller than 5.5 feet.’

This analysis can readily be extended to the equative if the ordering relation is properly adapted. Nevertheless, in the case of the superlative, the excessive, and the enough-construction, Yorùbá does not have any specialized morphology. To arrive at an English-like LF, one has to assume that ju and tó are lexically ambiguous. ju would therefore have at least three lexical entries: the comparative ones in (21) and (24), and one for the excessive¹³. We assume that the superlative uses a slightly modified version of (21) in which the standard of comparison is a set of salient alternatives – triggered by the focus on the compare – instead of one individual.

(26) ||ju_SUP|| = λg.λx[ _+ F]. max{d’|g(d’)(x)} > max{d|Ǝy ∈ Set[ _+ F] [g (d)(y)]}

In Yorùbá, degree-denoting expressions (of type ‹d›, for an alternative see Schwarzschild 2005), like ẹs^èbàtà márùn àt’ààb^ọ in (15), are accommodated by additional material, ní ìw^ọn in (15). Whether this additional material is to be considered as semantically vacuous in order to keep the relational meaning for the gradable predicate (see (19)), or whether this indicates that gradable predicates in Yorùbá should be given a different lexical entry remains an open question.

We have assumed a direct analysis of phrasal comparatives and showed which puzzles need to be solved in order to apply an English-like semantics to the Yorùbá data.

What about clausal comparatives in Yorùbá? A clear case of a clausal comparative in English, the comparative subdeletion, is rendered in Yorùbá with a bí… s, e-construction, see (27) ¹⁴. For English, it is assumed within the scalar approach that the than-clause provides a set of degrees (of type ‹d, t›, see Heim 2001) or a degree (Kennedy 1999: 143).

(27) tábìlì        yìí        gùn            jù            bí        lẹkùn    yẹn    ṣe        fẹ              lọ

Table                this      be.long    exceed    how    door      that    how    be.wide    sm

‘This table is longer than that door is wide.’

The bí… s, e-construction also appears in manner and degree wh-questions (see (28) and (17), respectively, báwo is decomposable into bí and wo), in embedded constructions about manner or degree ((29) is an embedded wh-question about degree). The syntactic status of the bí… s, e-construction seems to be that of an NP, since two bí… s, e-constructions are coordinated by àti, which is exclusively reserved to coordination of NPs (see (30)) ¹⁵.

(28) Báwo    ni       a       ṣe        ń           se         ìẹrsì? [Schleicher 2008: 125]

how. qm       foc    we    how    prog    cook    rice

‘How do we cook rice?’

(29) Nwọn    fẹ         mọ        b’ó          ti        ga           àti      b’ó          ti

They               want    know    how’it    prf    be.tall    and    how’it    prf

gùn    tó    [Rowlands 1969: 201]

be.long    reach

‘They want to know how tall and how long it is.’

(30) tábìlì    yìí      gùn           jù            bí         lẹkùn  yẹn    ṣe       fẹ              lọ   àti

table             this    be.long    exceed    how    door    that    how    be.wide   sm  and

bí        ọmọdé    yẹn    ṣe        ga            lọ

how    child        that    how    be.tall    sm

‘This table is longer than that door is wide and that child is tall.’

We leave this section with three puzzles for which more research is called for: (i) whether Yorùbá possesses clausal comparatives or not; (ii) how this bí… s, e-construction is to be interpreted, and (iii) whether the similarity in morphosyntactic marking between degree reference and manner reference should be reflected in the semantics. Regarding (ii), it should be noted that Mooré (Gur, Burkina Faso) and Hausa (Chadic, Nigeria) – both exceed-type languages – require a relative clause introducer (sẽn in Mooré, and yâddà in Hausa (Zimmermann 2009)) to build meaning equivalent to English clausal comparatives. This might suggest an analysis in the spirit of Beck et al. 2004 for (31) in Japanese, in which the standard of comparison – introduced by yori – is analysed as a (free) relative clause (see also Kennedy 2007b for discussion), i.e. as a set of individuals (to which a max operator is applied, see (32). The reader is referred to Beck et al. 2004 for details.)

(31) Mary-wa [John-ga kaite yori] (motto) takusan-no ronbun-o kaita

Mary-top John-nom wrote yori (more) many-gen paper-ACC wrote

‘Mary wrote more papers than John did.’

(32) max (λx. John wrote x)

In this section, we have shown which challenges a scalar approach applied to Yorùbá would have to overcome. But we have also left open many questions which should be further investigated before we can determine what kind of semantics the Yorùbá comparison constructions should be given. In section (3), we turn to the distribution of norm-relatedness.

3. Norm-relatedness

3.1. Characteristics of the contextually determined norm

In this section, we review the main characteristics of the norm which is referred to, for example, in the positive construction (see (2) repeated below).

(2) Nadjib    ga

Nadjib           be.tall

‘Nadjib is tall.’

We consider these characteristics to apply equally to both, the norm invoked in English and in Yorùbá.

(i) The norm can vary, and this variation affects the truth-conditions of the sentence.

The positive construction in (2) can thus receive a different truthvalue even if the facts about Nadjib are not manipulated. The variation of the norm primarily depends on the variation of the comparison class, i.e. a set of individuals which forms a natural class. The norm corresponds to the average value to which the individuals of the comparison class possess the property in question (but see Kennedy 2007a for refinements). The comparison class is typically made explicit in English by a for-PP. In Yorùbá, the same strategy is used. Therefore, if we assume that Nadjib measures 1 meter 50, (2) is true with the PP for a child, but is considered false with the PP for an adult.

(ii) The norm is (usually) vague, i.e. it is not assigned to a definite degree.

The positive construction in (2) is vague (Kennedy 2007a, a.o.). It is possible to manipulate the context (by changing the comparison class) such that the truth value of (2) is not clearly determined, i.e. Nadjib would be in this context a borderline case for the application of ga, ‘be tall’. We ascribe the vagueness of (2) to the vagueness of the norm. Note that for gradable predicates associated with a measurement system, it is possible to render the norm precise. Imagine e.g. that you are allowed to use in your CV the predicate gifted only if you have an IQ of 130 or more. In such a context, gifted and the norm on which its application is based are not vague.

(iii) Negative polar gradable predicates (like e.g. short) do not share the same norm as their positive polar counterparts (tall).

In a given context, the fact that the tree referred to in (33) is not tall (i.e. it does not satisfy the norm for applicability of the gradable predicate tall) is not sufficient to accept (33) as true, as is shown by the felicity of sentence (34).

(33) This tree is short

(34) This tree is neither tall, nor short

(iv) A contextually determined norm is only relevant for a subclass of gradable predicates.

The truth-conditions of some gradable predicates – called ‘absolute’ by Kennedy & McNally 2005 – do not depend on a contextually determined norm. For example, (35) is true even if the road is minimally wet, i.e. the norm does not vary, but is lexically fixed to a minimun.

(35) This road is wet

Predicates like straight, closed, etc. are true of an individual if that individual possesses the gradable property fully, i.e. in this case the norm is set to a maximum. In other words, a road is already wet if it is only partly wet, whereas it is not straight if it is only partly straight. Both adjective types – i.e. minimal and maximal ones – are absolute gradable predicates which do not depend on a contextually determined norm, but on one that is fixed lexically. It should be noted that reinterpretation is possible, i.e. an absolute gradable predicate can be used to sharpen what counts as the norm in a context with the consequence that subsequent uses of the same predicate in this context are based on the newly sharpened norm (see Barker 2002 for details). Imagine a situation in which Bob and Bill are discussing what can be considered as straight. Bob shows a road to Bill and say: “look at that road, that is straight”. Bob’s utterance specifies the range for the applicability of the gradable predicate straight.

In this case, the predicate is thus used to sharpen the norm. In this section, we have introduced the four main characteristics of the contextually determined norm. We now turn to the distribution of norm-related readings.

3.2. Distribution of norm-related readings

In this section, we first deal with the following two questions: (i) What is a norm-related reading?; (ii) How can it be diagnosed?

(i) We consider a construction to be norm-related if a contextually determined norm is invoked in its truth-conditions.

(ii) The basic test used in the literature (Bierwisch 1989, Rett 2008) to detect norm-relatedness is the entailment test.

The norm-relatedness of a construction can be detected through its entailments (Bierwisch 1989: 90). If a construction entails one of its corresponding positive constructions, it is norm-related¹⁶. We thus have to test whether e.g. (37) entails (38) in order to find out whether (37) is norm-related. We call (38) the norm-related entailment of (37).

(37) Barbara is as short as Naomi

(38) Naomi is short

Entailments cannot be cancelled. Such a cancellation results in contradiction (39).

(39) If S₁ entails S₂, then S₁ ˄ not S₂ is a contradiction.

To diagnose norm-relatedness, the construction to be tested is set in a context that is manipulated such that it entails the negated version of (38). If this results in contradiction, the construction is considered to be norm-related.

A remark is in order here. According to Matthewson (2004: 399) it is possible to reliably elicit two types of semantic judgments: judgments about truth values and judgments about felicity. We assume that it is also possible to reliably elicit contradiction judgments, since these can be considered as a subcategory of truth value judgments. Language assistants nevertheless do not judge sentences like (40) as contradictory, but rather as infelicitous. The test is, however, not invalidated, since we can interpret this infelicity as stemming from the norm-relatedness of the left conjunct.

(40) #Barbara is as short as Naomi, but, actually, Naomi is not short¹⁷

We can next turn to the actual distribution of norm-relatedness. Chart 1 indicates for 12 different comparison constructions, whether they are norm-related (+) or not (–). The investigated constructions are the positive (pos), the comparative (comp), the equative (eq), degree questions (dq), the excessive (exc), and the enough-construction (enough). For each construction, both the positive polar (pos) and the negative polar (neg) gradable predicates have been considered. The data come from different sources: English (Rett 2008), German (Bierwisch 1989), Russian (Krasikova 2009); the Yorùbá data are based on elicitation done by the present author with four language assistants (see footnote 1). (‘#₁’  / ‘#₂’) in the fifth column means that for #₁ language assistants the construction is norm-related, whereas it is not norm-related for #₂ language assistants. Thus e.g. the Yorùbá counterpart of the equative construction with a negative polar gradable predicate in (41) is judged to be norm-related by four language assistants and not norm-related by none¹⁸.

Constructions	English	German	Russian	Yorùbá
[pos][pos]	+	+	+	+
[neg][pos]	+	+	+	+
[pos][comp]	–	–	–	– (0  / 4)
[neg][comp]	–	–	–	– (1  / 3)
[pos][eq]	–	–	+	– (0  / 4)
[neg][eq]	+	+	+	+ (4  / 0)
[pos][dq]	–	–	+	– (0  / 4)
[neg][dq]	+	+	+	+ (4  / 0)
[pos][exc]	–	–	+	– (0  / 4)
[neg][exc]	–	–	+	– (1  / 3)
[pos][enough]	–	–	+	– (0  / 4)
[neg][enough]	–	+	+	– (1  / 3)

Chart 1: Distribution of norm-relatedness across comparison constructions

As mentioned above, we use the entailment test to diagnose normrelatedness in Yorùbá.

(41) Adé        kúrú          tó          Bùnmi

Adé                be.short    reach    Bùnmi

‘Adé is as short as Bùnmi.’

At least three facts can be learned from Chart 1.

First, regarding English, German, and Russian we can observe that:

(i) English and German pattern quite similarly.

They only differ in the enough-construction with negative polar predicate. This difference might be the reflex of the absence of a unified elicitation technique for norm-relatedness. The fuzziness of the judgments might also indicate that some constructions are only weakly norm-related (see section (3.3.3.)).

(ii) English/German and Russian pattern very differently.

In Russian, norm-relatedness is present in almost all comparison constructions. The only construction that is not norm-related is the (synthetic)¹⁹ comparative construction, as in (42).

(42) Germann    byl      sil’nee       čem      ego   protivnik   [Rett 2008: 109]

Germann             was    stronger    what    his    adversary

‘Germann was stronger than his adversary.’

(iii) Yorùbá patterns like the English/German group.

Although Yorùbá does not pattern morphosyntactically like English and German (see section (2.1.)), it shows a quite similar distribution of norm-related readings.

The same language assistant produced a judgment departing from the three others in the case of the negative comp, exc, and enough constructions. We can think of two possible interpretations for this variation. This variation might be due to hypercorrection, i.e. a case in which an language assistant – trying to help the researcher – deliver judgments which offers a neater pattern than it really is. A second possibility is that this variation might reflect speaker uncertainty. We consider the first possibility to be the more plausible one in this case. Nevertheless, it should be noted that the possibility of hypercorrection attests to the weakness of the effect.

We have not enough data from other exceed-type languages to be able to make any generalization extending to this category of languages. It should be the subject of further research to investigate whether or not exceed-type languages pattern alike with respect to the distribution of norm-related readings.

3.3. Predicting the distribution of norm-related readings

In this section, we review which factors might be held responsible for the distribution of norm-relatedness. First, we exclude determination by individual factors. Second, we introduce Rett’s 2008 account of the distribution of norm-relatedness in English and show its shortcomings. We then introduce Krasikova’s 2009 attempt to unify in one account both the English and the Russian distribution of norm-relatedness. Finally, we consider what the Yorùbá data might yield for the theorizing about the distribution of norm-related readings.

Considering the distribution of norm-relatedness in English/German/ Yorùbá in Chart 1, it is evident that it cannot be exclusively determined by one of the following three factors (i) to (iii):

(i) the gradable predicate used, since (44) is norm-related, whereas (45) is not;

(44) John is tall²⁰

(45) John is taller than Bob

(ii) the polarity of the gradable predicate, since (46) is norm-related, whereas (47) is not;

(46) John is as small as Naomi

(47) John is smaller than Naomi

(iii) the type of comparison construction involved, since (48)²¹is normrelated, whereas (45) is not.

(48) Jones is happier than Noam

3.3.1. Rett’s account (Rett 2008)

On the basis of such observations, Rett 2008 proposes that the distribution of norm-relatedness in English results from the interplay of two (binary-valued) factors:

(i) the polarity, i.e. whether the gradable predicate is positive or negative polar;

(ii) the type of comparison construction involved. According to Rett, a comparison construction can be directional versus non-directional²².

A comparison construction is non-directional if the modification of the ordering relation which it encodes does not affect its truth-conditions. To modify the ordering relation of a comparison construction only means – on Cresswell’s (1976: 284) assumptions – choosing the gradable predicate of opposite polarity. Thus degree questions are e.g. non-directional, since truth-conditions are not affected by the modification of the ordering relation, see (49). The same is not true of the comparative whose truthconditions are affected by such a modification, see (50). The comparative is therefore directional.

(49) ‘How tall is Sam? ‘ is truth-conditionally equivalent to ‘How short is Sam?’

(50) ‘John is taller than Sam’ is not truth-conditionally equivalent to ‘John is shorter than Sam’

The interplay of these two factors produces four possible combinations. From these only comparison constructions which feature a negative polar gradable predicate and are non-directional are norm-related:

directionality polarity	Directional	Non-directional
Positive	–	–
Negative	–	+

Chart 2: Distribution of norm-related readings predicted by Rett’s 2008 account

Three additional ingredients effect the observed distribution of normrelatedness in English in Rett’s 2008 system:

(i) every comparison construction is potentially ambiguous between a norm-related, and a non-norm-related reading;

(ii) negative polar gradable predicates are marked relative to their positive counterpart;

(iii) truth-conditionally equivalent propositions enter a (semantic) competition whose outcome is to block the availability of the marked candidate.

As an illustration, we show how the norm-relatedness of the equative construction is derived in this account.

First, both the positive polar and the negative polar equatives are potentially ambiguous between a norm-related and a non-norm-related reading, see Chart 3. Only the non-norm-related readings are truth-conditionally equivalent (=)²³. Truth-conditionally equivalent propositions enter a competition, such that the marked candidate, i.e. in this case the candidate featuring a negative polar gradable predicate, is blocked, see Chart 4. The negative polar equative is thus not ambiguous, but can only receive a norm-related reading, whereas the positive polar equative remains ambiguous. Only those constructions which are unambiguously normrelated are considered norm-related. Thus the negative polar equative is norm-related, whereas the positive polar equative is not norm-related.

John is as tall as Sam		John is as short as Sam
+	≠	+
–	=	–

Chart 3: Potential ambiguity of both negative and positive polar equatives

John is as tall as Sam		John is as short as Sam
+	≠	+
–	=	blocked

Chart 4: Outcome of the semantic competition

This account – if we accept that the comparative, the excessive, the enough-construction, and the superlative are directional, whereas the equative and degree questions are not – correctly derives the distribution of norm-relatedness in English²⁴ according to the pattern shown in Chart 1. We nevertheless point at two potential problems.

First, the notion of markedness should be refined. As it is, it derives that (51) and (52) (Rett 2008: 116) are both equally marked compared to each other. (52) uses short which is marked compared to tall, whereas (51) uses less which is marked compared to more. Intuitively, it nevertheless seems that (52) is more marked overall than (51).

(51) Adam is less tall than Doug

(52) Adam is more short than Doug

We therefore need a more fine-grained approach to the notion of markedness.

The Russian data pose an additional problem to Rett’s account. The distribution of norm-relatedness is not correctly predicted by her system.

3.3.2. Krasikova’s account (Krasikova 2009)

Krasikova’s 2009 account attempts to predict both the distribution of norm-relatedness in English/German and in Russian. She suggests that gradable predicates are lexically ambiguous between two meanings: a vague meaning, and a scalar meaning. Norm-relatedness arises from the use of the vague meaning of a gradable predicate, i.e. the distribution of norm-relatedness is recast as the distribution of the vague meaning for the gradable predicate.

Krasikova assumes that different factors influence the distribution of vague meaning for gradable predicates in English and in Russian. In Russian, the scalar meaning needs to be licensed by degree morphology on the gradable predicates. Since it is only in the case of the (synthetic) comparative that degree morphology is visible on the gradable predicate, it is correctly predicted that only this construction is norm-related. In English, on the other hand, another factor drives the resolution of the ambiguity between vague meaning and scalar meaning: if two constructions are truth-conditionally equivalent (in one of their readings) and only differ in the polarity of their gradable predicate, it is assumed that this reading is blocked for the marked counterpart, and therefore not available anymore. For example, (53) and (54) are truth-conditionally equivalent if we consider the scalar meaning for their gradable predicates and under an exactly-reading for the equative. Since (54) is marked compared to (53), the scalar meaning is blocked for (54). As a result, (54) only retains its vague meaning and is therefore norm-related.

(53) Naomi is as tall as Jim

(54) Naomi is as short as Jim

Differing in the implementation, Krasikova’s account nevertheless posits – as Rett’s does – the relevance of polarity for English. It also assumes that negative polarity is marked compared to positive polarity.

3.3.3. What does Yorùbá contribute to this picture?

How can the empirical picture delivered by the Yorùbá data help refining or correcting the existing approaches to the distribution of normrelated readings?

The main import is the fact that surface morphosyntax cannot be held responsible for the distribution of norm-relatedness, since a language with a very different surface, Yorùbá, patterns like English/German. On the other hand Russian, which is morphosyntactically closer to English/ German, shows a completely different distribution of norm-relatedness.

Secondly, we suggest that the minor judgment differences found in Yorùbá and between English and German (see Chart 1) might suggest that norm-relatedness is not always a clear-cut phenomenon. There is a decrease in ‘norm-relatedness strength’ between the positive construction and the enough-construction, i.e. norm-relatedness is a graded phenomenon. This is corroborated by the fact that judgments for the enough- construction are quite shaky (see Chart 1). This might be the reflex of the need for methodological refinements in the elicitation of normrelatedness. We assume that it is also the reflex of the gradedness of the phenomenon. Moreover, language assistants do not always react to the entailment test (see (3.2.)) by judging a sentence whose norm-related reading is in contradiction with its context as contradictory. See the judgment elicited for (40) according to which the sentence is infelicitous. If we consider that language assistants can discriminate between contradictory sentences and infelicitous sentences, it indicates that norm-relatedness is not in all cases a truth-conditional phenomenon. We suggest that the gradation of the norm-relatedness has not been taken enough into account in Rett 2008 and Krasikova 2009. In both accounts the phenomenon is encoded as a binary phenomenon and not as a graded phenomenon.

4. Conclusion

In this paper, we have pursued three goals: introduce the main characteristics of the comparison constructions in Yorùbá (section (2.1.)), apply a scalar analysis to the Yorùbá data (section (2.2.)), and give an account of norm-relatedness in Yorùbá (section (3)).

Regarding the characteristics of comparison constructions in Yorùbá, we conclude that: (i) Yorùbá expresses comparison using a serial verb construction involving a predicate which encodes the dimension, and a predicate encoding the ordering relation. (ii) There is no specialized morphology to express comparison. The only lexical item which might be considered to be specialized is lọ. (iii) Yorùbá allows direct reference to measurements, as shown e.g. in (15). It is nevertheless interesting to note that these references seem to be accommodated by additional materials ní ìw^ọn in (15) and fi in (16). (iv) English clausal comparatives are expressed in Yorùbá through bí … s, e-constructions which display characteristics of nominals. It might therefore be the case that Yorùbá lacks a ‘real’ clausal comparative. It should be mentioned that characteristics (i) and (ii) are quite widespread among African languages and might therefore be areal phenomena (Leyew & Heine 2003).

We applied a scalar analysis to the Yorùbá data in a straightforward manner. We gave Yorùbá gradable predicates the same lexical entry as the one reserved for English gradable predicates, and we assigned the meaning of the English comparative morpheme -er to the predicate ju. We adopted the direct analysis of Heim 1985. Since we do not have evidence for the existence of clausal comparatives, we tentatively hypothesize that Yorùbá only requires the 3-place comparative morpheme type such as in (21) and its akin variants (e.g. (24)), i.e. no morpheme of the type ‹‹d, t›, ‹‹d, t›, t›› is necessary for the compositional analysis of comparison in Yorùbá (see also Bhatt & Takahashi 2007). This step would predict that there is no scope interaction between the comparative morpheme and other operators (see footnote 12).

Our third goal was to explore the distribution of norm-relatedness in Yorùbá. We found that English, German, and Yorùbá pattern quite similarly in this respect, whereas Russian does not. Such a language grouping suggests a modelling of the phenomenon which does not refer to morphosyntax, since morphosyntactically distant languages such as English/ German and Yorùbá can pattern alike with respect to the distribution of norm-related readings. We also suggested that norm-relatedness is a graded phenomenon instead of a binary phenomenon. It has a truth-conditional effect in most of its occurrences, but it is not always truth-conditional.

Acknowledgements

This research is part of the project B17 of the SFB 441 “Linguistische Datenstrukturen” which is funded by the Deutsche Forschungsgemeinschaft. We would like to thank Bùnmi Aina, Akin Akinleye, Isaiah Okere, and Nadjib Sadikou for their patience during (sometimes long) elicitation sessions. Vera Hohaus and Paul Peterson also helped me with their intuitions about the German and English data. Additionally I am grateful for the comments by Sigrid Beck, Remus Gergel, Stefan Hofstetter, and Sveta Krasikova. All remaining errors are, of course, mine.