Explaining alienability contrasts in adpossessive constructions: Predictability vs. iconicity

Abstract This paper argues that alienability contrasts in adnominal possessive constructions should not be explained by iconicity of distance, but by predictability due to the higher relative frequency of possessed occurrences of inalienable nouns. While it is true that when there is an alienability split, the alienable construction typically has an additional marker which often separates the possessor from the possessed noun, the broader generalization is that additional marking is found when the possessive relationship is less predictable. This generalization also extends to cases of antipossessive marking and impossessibility. The diachronic mechanisms responsible for the development of alienability contrasts are differential reduction and differential inhibition of a new construction.


The explanation in a nutshell
In this paper, I propose that the universals of form-function relationship in alienability contrasts should not be explained in terms of iconic motivation, as in Haiman's (1983; influential work, but by predictability due to the different usage frequencies of different constructions (what is called "economic motivation" by Haiman). Consider a typical alienability contrast in an adpossessive (adnominal possessive) construction, from the West Papuan language Abun: (1) Abun (Berry & Berry 1999: 77-82) a. alienable possession ji bi nggwe I GEN garden 'my garden' b. inalienable possession ji syim I arm 'my arm' We see that in this language, an adpossessive construction with an alienable noun (such as 'garden') requires a possessive (genitive) postposition, while a construction with an inalienable noun (a body-part term) expresses possession by mere juxtaposition. This pattern is common across languages (e.g. Nichols 1988;Chappell & McGregor 1996;Stolz et al. 2008).
According to Haiman's (1983; explanation in terms of iconic motivation, the juxtaposition construction chosen for inalienable possession shows little "linguistic distance" between possessor and possessed noun, and this iconically reflects the greater CONCEPTUAL CLOSENESS between possessor and possessed item (supposedly arms are not conceived of independently of their owners). By contrast, the overt genitive marker bi between the possessor and the possessum in the alienable 'my garden' exhibits greater linguistic distance, and this reflects the greater conceptual distance between 'garden' and 'I'.
My explanation is quite different from Haiman's in that it makes no reference to iconicity, but only to frequency of use, hearer expectations (= predictability) and length of coding. It starts with the observation that nouns like 'arm' normally, or at least very frequently, occur as possessed nouns in possessive nominal phrases, whereas for nouns like 'garden', this is much less frequent: We often talk about gardens without mentioning or even thinking about their possessors. As a result of this difference, the overt expression of the possessive relationship is more expected or predictable with nouns like 'arm'. Languages like Abun exploit this redundancy and use an overt possessive marker only with nouns like 'garden', while body-part terms occur in a shorter markerless construction. The contrast in (1) can thus be subsumed under the form-frequency correspondence principle, as this regularity is called in Haspelmath et al. (2014) and Haspelmath & Karjus (2017).
In this paper, I first define the comparative concepts required to compare languages in the relevant respects ( §2), and then contrast the two explanations in §3, where I also justify the claim that there is a frequency difference. The most salient phenomenon, the overt vs. zero alienability contrast as seen in (1), follows from both explanations, and in §4 I discuss a few further predictions that are made by both approaches. But then in §5 and §6 I show that there are further tendencies that either go against Haiman's iconicity explanation or are not predicted by it, while they follow from my predictability explanation. In §7, I formulate the observed generalizations in the most general terms, in the spirit of Greenbergian universals and making references to a novel possessibility scale. After a brief discussion of the difference between relative and absolute frequencies ( §8), I end with some discussion of the diachronic pathways which give rise to the observed coding asymmetries. It should be noted at the outset that the cross-linguistic generalizations formulated in this paper are not based on a systematic study of a sample of languages, but on a close reading of the rich typological literature (e.g. Ultan 1978;Nichols 1988;Chappell & McGregor 1996;Heine 1997;Koptjevskaja-Tamm 2003;Nichols & Bickel 2005a;2005b;Stolz et al. 2008;Dixon 2010;Aikhenvald 2013;van Rijn 2016a). It is thus a very plausible hypothesis that the generalizations are true and will be confirmed by additional data. Gathering such data systematically and publishing it in the form of a database is a desideratum for future research, and it is hoped that the present paper's hypotheses will serve as further inspiration for such research. Moreover, this paper should not be read as a critique of John Haiman's decades-old work, which I have long found very inspiring. I merely use Haiman's old proposal as a concrete representative of a kind of explanation that has been widely adopted and that I think can and should be improved upon.

Definition of key comparative concepts
To compare possessive constructions across languages, one first needs to carefully define a set of comparative concepts in terms of which the comparison is carried out (cf. Haspelmath 2010). In this paper, a POSSESSIVE RELATIONSHIP is defined as a relationship of ownership (e.g. 'my garden'), a kin relationship (e.g. 'my father'), or a part-whole relationship (e.g. 'my arm', 'the branch of the tree'). This follows previous work in typology, in particular Koptjevskaja-Tamm (2003).
This definition may raise some questions. It is not immediately evident that ownership, kinship and part-whole are a natural class of meanings, and it is not easy to formulate a common denominator for them. Moreover, in most or all languages, (some of) the constructions used to express ownership, kinship and part-whole are also used for other relationships, such as 'my school' or 'my report'. Clearly, any kind of concept that subsumes all of the relationships must be very abstract. According to Langacker (1993;, possessors in possessive constructions provide REFERENCE POINTS by which the hearer can get mental access to the possessum. This seems like an insightful analysis, but it is not useful as a basis for cross-linguistic comparison, because the highly abstract concept of a reference point cannot be clearly delimited. By contrast, kinship and part-whole relationships are easily identified, and ownership does not pose serious problems either. These three relationships seem to be a good basis for cross-linguistic comparison, as they allow us to state interesting cross-linguistic generalizations (see §3-7). 1 The two entities in a possessive relationship are the POSSESSOR (the owner, the kinship ego, or the whole) and the POSSESSUM (the owned thing, the ego's relative, or the part).
An ADPOSSESSIVE CONSTRUCTION (short for adnominal possessive construction) is a construction in which a possessive relationship is expressed in a single nominal (or NP) consisting of (i) a noun expressing the possessum (the possessed noun) and (ii) a modifying possessor nominal or a possessive person index (i.e. a bound person form). Thus, while possessive relationship is a semantic notion, adpossessive construction is a syntactic notion, which presupposes that nominal phrases can be identified across languages. By extension, a construction that has the same form in a language as an adnominal construction expressing possession (in the narrow sense of the preceding paragraph) may also be called an adpossessive construction (e.g. my school or my report in English, which have the same form as my garden, my father or my arm but express relationships other than ownership, kinship or part-whole).
Adpossessive constructions contrast with predicative possessive (predpossessive) constructions such as I have a garden, with belonging-constructions such as This garden is mine, and with external possessor constructions, such as (2).
(2) German Die Mutter wusch dem Kind die Haare. the mother washed the.DAT child.DAT the.ACC hairs.ACC 'The mother washed the child's hair.' External possessor constructions (cf. König & Haspelmath 1998;Payne & Barshi 1999) are constructions in which the possessor has the form of a clause-level argument but 1 By starting out from the three semantic groups of noun meanings, I adopt an approach that is in a way the opposite from the following statement by Stolz et al. (2008: 31): "If a language is subject to a formal distinction of alienable and inalienable possession, then either kinship roles or body parts form part of the paradigm of inalienable possessees" (cf. also Nichols 1992: 572 for a similar statement). The problem here is that there is no good definition of "alienable/inalienable" that does not make any reference to the three semantic groups. semantically modifies another argument in the same way as an adnominal possessor does. Neither predicative nor external possessor constructions are considered in this paper. 2 An ADPOSSESSIVE SPLIT is a situation in which different classes of referential expressions require (or strongly favour) different adpossessive constructions. In a POSSESSOR-DETERMINED SPLIT, different kinds of possessor occur in different constructions, as can be illustrated again from German in (3). In this language, personal pronouns require a construction with a prenominal possessor (3a), proper names favour it (3b), and full nominals (largely) exclude it (3c). But splits may also be DETERMINED BY THE POSSESSUM NOUN, and it turns out that in such cases, ownership vs. kinship and/or ownership vs. part-whole is typically a crucial contrast. An ALIENABILITY SPLIT is a possessum-determined split in which kinship terms and/or body-part terms behave differently from other kinds of possessed nouns occurring in an ownership relationship. We already saw an example in (1), and (4) gives another example of an alienability split.
(4) Jeli (Mande; Tröbs 1998: 167-169) a. Soma ra monbilo (*Soma monbilo) Soma of car 'Soma's car' b. Soma bulo-ni (*Soma ra bulo-ni) Soma arm-PL 'Soma's arms' When a language exhibits an alienability split, we say that a construction used characteristically with kinship and/or body-part possessed nouns is an INALIENABLE POSSESSIVE CONSTRUCTION, while a construction that is characteristically NOT used with kinship and/or body-part possessed nouns is called an ALIENABLE POSSESSIVE CONSTRUCTION. 3 Thus, in (1) and (4), the (a) examples are alienable constructions, while the (b) examples are inalienable constructions. When a language has two constructions of this kind, we can say that it makes an alienability contrast, and we can call the nouns occurring in the inalienable construction inalienable nouns, and those occurring in the alienable construction alienable nouns. In general contexts, not referring to particular languages, I will also use these terms as abbreviations for body-part/kinship terms and other nouns, respectively.
It should be noted that this definition of (in)alienable construction, which is based on that of an alienability split (and thus ultimately on different classes of possessed nouns), is quite different from another widespread understanding of the contrast in terms of different SEMANTIC RELATIONS, e.g. "Inalienable possession is generally seen as involving a fairly stable relation over which possessors have little or no control, alienable possession as comprising a variety of less permanent, more controlled relationships." (Hollmann & Siewierska 2007: 410) The trouble with such semantic definitions is not only that they involve highly abstract relations that are difficult to verify cross-linguistically, but also that in the great majority of cases, differential coding of possessive constructions takes the form of splits, not of fluid alternations (cf. Nichols 1988: §5). The inalienable/alienable opposition is not at all like that between singular and plural, or between past and future tense, which are semantic feature values that (in principle) any noun or verb can take. But even though some languages show some flexibility (see also §6.3.1), in general the difference between alienable and inalienable possession is simply a constructional split, with no clear semantic implications, not unlike the split between pronouns in English (which make a nominative/accusative distinction) and nouns (which do not). 4 Another common way of conceiving of the alienability distinction is in terms of inherent relationality, with possessors in inalienable constructions being arguments, and alienable possessors being modifiers (Lehmann 1983; van Rijn 2016a: §2.2). Again, this conception is not wrong, but it is very difficult to pin it down. Artifact nouns like 'chair' and 'school' are like body-part terms in that they always belong to someone and would hardly exist without their users.

The explanandum: Overt vs. zero alienability contrasts
On the basis of the comparative concepts of §2, we can formulate a universal generalization: 3 Note the inclusion of "characteristically" in the definition: In some languages, constructions that are primarily used with kinship and/or body-part terms can also be used for a few other nouns. This does not seem to be systematic, however, so I will not say anything further about such atypical inalienably used nouns. I will also ignore cases where the semantic groups of nouns do not correspond to the semantic type of relationship, in particular where body parts are owned (e.g. ‚my tail', when the speaker talks about a an animal tail she owns). 4 Nichols & Bickel (2005b) therefore use the term "possessive classification", which is basically the same as my possessive split, but has the disadvantage of suggesting that possessive classifiers are involved.
(5) Universal 1: If a language has an adnominal alienability split, and one of the constructions is overtly coded while the other one is zero-coded, it is always the inalienable construction that is zero-coded, while the alienable construction is overtly coded.
That this generalization is well-supported has been known for some time (Ultan 1978: 26;Haiman 1983;Nichols 1992: 122;Heine 1997;more recently van Rijn 2016a). Some examples of languages with an alienability split that show a coding asymmetry (i.e. an overt vs. zero contrast) are given in (6) Li & Thompson 1981: 113, 115) a. tā-de chènshān he-GEN shirt 'his shirt' b. tā (-de) māma he(-GEN) mother 'his mother' (12) Tommo So Dogon (Plungian 1995: 35) a. tigɛ wo mɔ name he GEN 'his name' b. u ba you father 'your father' Not all cases of alienability splits show a coding asymmetry, as can be seen in example (13), where both possessive constructions use an overt marker, a for alienable and o for inalienable possession. However, such cases are not counterexamples to Universal 1, because this makes claims only about alienability splits with a coding asymmetry.
(13) Samoan (Oceanic; Mosel & Hovdhaugen 1992: 282-90) a. le naifi a le fafine the knife of the woman 'the woman's knife' b. le uso o le fafine the sister of the woman 'the woman's sister' I am not aware of exceptions to Universal 1, so this appears to be a very strong crosslinguistic generalization. Of course, it makes a claim only about alienability splits, and many (perhaps most) languages do not show alienability splits. But alienability splits are widespread, occurring in all continents and in many different language families, so an explanation of Universal 1 would be quite significant for our understanding of language. The next two subsections discuss two explanations that have been proposed, and in the remainder of the paper I will argue for the second explanation.

The iconicity explanation
As was briefly summarized in the introductory section, Haiman (1983) advanced an explanation in terms of iconicity of distance. He proposed a general iconic principle which says that "The linguistic distance between expressions corresponds to the conceptual distance between them" (1983: 782). One instantiation of this is the alienability contrasts seen in (1), (4), and (6)-(12) above. Haiman writes that "...two concepts are close to the extent that they are perceived as inseparable (e.g. there is a closer conceptual link between a possessor and an inalienably possessed object than between a possessor and an alienably possessed object)" (1983: 783).

The predictability explanation
The competing explanation in terms of predictability which I propose in this paper is not based on the conceptual or semantic difference between the two construction types, but on the difference in terms of usage. A fact that has not often been noted is that there is a significant DIFFERENCE IN FREQUENCY of occurrence in the two types of possessive construction: Inalienable nouns (=bodypart/kinship terms) very often occur as possessed nouns, whereas alienable nouns occur as possessed nouns much more rarely. This is not a surprising claim -no linguist would be astonished to hear that nouns like 'foot' and 'sister' occur more frequently in possessive nominals (e.g. your foot, Lee's sister) than nouns like 'tree' or 'knife'. But interestingly, few linguists have made reference to frequency of use in explaining the contrast, and few have even commented on the difference (though Nichols (1988: 579) notes that inalienable nouns are "those nouns which are most often possessed"; cf. also Nichols (1992: 121)).
The explanatory principle here is Zipfian economy (Zipf 1935;Haspelmath 2008a). It has been shown to account for a wide variety of form asymmetries which correspond to frequency asymmetries (e.g. Greenberg 1966;Croft 2003: Chapter 4; Hawkins 2014: §2.2). Following Haspelmath et al. (2014: 592), the specific principle as applied to grammar can be formulated as in (14).

(14) The grammatical form-frequency correspondence principle
When two minimally different grammatical patterns (i.e. patterns that form an opposition) occur with significantly different frequencies, the less frequent pattern tends to be overtly coded (or coded with more coding material), while the more frequent pattern tends to be zero-coded (or coded with less coding material).
Some further grammatical oppositions for which this principle has been shown to make correct predictions are listed in (15) (for the last three, see Croft 1991). This is thus a very broadly applicable principle with great explanatory power.
(15) present/future, 3rd person/2nd person, nominative/accusative, active/passive, affirmative/negative, masculine/feminine, positive/comparative, attributive adjective/predicative adjective (including copula), predicative verb/nominalized verb, action word/agent noun The causal chain that I hypothesize is responsible for the systematic coding asymmetry is schematized in (16). The idea is that, upon hearing an inalienable noun, hearers can predict that it will occur as possessed noun in a possessive construction, and overt marking of the possessive relationship is relatively redundant. This redundancy is exploited in some languages by using less explicit coding for possessive constructions with inalienable possessed nouns.
(16) frequent → predictable → less need for coding Since the coding asymmetry is universal (as a tendency), the explanation only works if the frequency asymmetry is also a universal tendency. Conclusively demonstrating that this is the case would require corpus data from a large number of languages, which would be a very expensive enterprise. In this paper, I limit myself to a few manually coded examples, 20 occurrences of 12 nouns (six inalienable, six alienable) from three fairly different languages, Biblical Hebrew, Ancient Greek, and English, shown in Table 1 (see also Haspelmath 2008a: 19, andHaspelmath 2014: 206, for some preliminary data). The purpose of this table is merely to give initial plausibility to the claim.
Like the grammatical universals, the claim that the frequency asymmetry is universal thus has the status of a very plausible hypothesis that would ideally be confirmed with a more complete and more carefully selected dataset. As a reviewer noted, the languages used to illustrate the frequency asymmetry do not have an alienability contrast in their grammar. This is actually good, because it means that a conceivable alternative explanation can be ruled out, namely that the direction of causation would be the reverse, with the higher frequency of possessed occurrences of inalienable nouns being due to the shorter coding. As can be seen in Table 1, the general trend is very strong, but there are also notable individual differences between different nouns. The fact that in general, all kinship terms and all part-whole terms in a language behave in the same way grammatically must be due to some kind of (presently not well-understood) system pressure, as discussed in Haspelmath (2014). Clearly, grammatical systems of languages do not reflect frequency differences very closely, but tend to work in terms of broad discrete classes which are defined semantically.

Distinguishing between the iconicity explanation and the predictability explanation
For the data that we have seen so far, the iconicity and the predictability explanation make the same predictions, so either of them (or indeed both) could be correct. In the next three sections, I will make a number of additional observations concerning the form of adpossessive constructions in the world's languages. We will see that there are some phenomena where both types of explanation make the same or similar predictions ( §4), but also one phenomenon where the iconicity explanation makes a wrong prediction ( §5), and some phenomena that follow from the predictability explanation but not from iconicity ( §6). The generalizations seen in §5-6 thus crucially favour the predictability explanation over the iconicity explanation, and we can abandon the concept of iconicity in explaining alienability splits. Haiman (1983) proposes a "scale of linguistic distance", shown in (17), consisting of four kinds of constructions representing four types of linguistic distance (or cohesion) between parts of the construction, which according to him correspond to different degrees of conceptual distance.

The cohesion scale
(17) Haiman's (1983: 782) I call this scale cohesion scale rather than "distance scale", because (ii) and (iii) do not differ in distance in the sense of something intervening between X and Y. While we often write a space between two elements which are not "bound", there is not actually a pause between them, and the notions of free vs. bound expression, or single-word vs. multipleword expression, are poorly understood (Haspelmath 2011a). But intuitively, "bound expression" is more cohesive than "juxtaposition". The notion of distance is not really applicable to (iv) (where there is no X and Y whose distance could be measured), but again, expression by Z is intuitively more cohesive than expression by X-Y.
Haiman applies this scale to a number of grammatical contrasts, among them alienability contrasts. He makes the claim in (18), which he attributes to "Joseph Greenberg (p.c.)" (Haiman 1983: 793).
(18) The Haiman-Greenberg Alienability Universal "In no language will the linguistic distance between X and Y be greater in signaling inalienable possession, in expressions like 'X's Y', than it is in signaling alienable possession." This universal is stronger than my Universal 1 in (5)

Bound vs. free expression
The first prediction of (18) does indeed seem to be correct. It can be formulated as in (19)  'my mother' (Khizanishvili 2006: 12-13) Universal 2 is predicted by Haiman's iconicity explanation, but it is also expected from the predictability explanation. More predictable forms are shorter (see §6.1 below), and shorter forms have a greater tendency to coalesce with a host, apparently for phonological reasons (though the details are not fully clear; see Haspelmath 2011b for some discussion). Thus, Universal 2 cannot be taken to favour the iconicity explanation over the predictability hypothesis. 5

Separative vs. cumulative expression
The universal in (18) also makes a prediction that Haiman does not mention: Inalienable nouns should show a tendency to fuse with their possessors into a single unanalyzable (i.e. cumulative) form. And indeed, with kinship terms we occasionally find suppletive cumulative forms such as Lakota ina 'my mother' (instead of the expected *mi-hų), Juhoan áíá 'my mother', and Daai Chin nääi 'my mother' (a further example from Ungarinyin is cited by van Rijn (2016b: 7); see also Vafaeian (2013)  However, cumulative expression is not characteristic of inalienable possession as such, but only of forms with high absolute frequency. This is a very general property of suppletion (Ronneberger-Sibold 1988;Hippisley 2001): In all languages, suppletion tends to occur in the most frequent lexical items, and 'mother' happens to be very frequent in absolute terms.
By contrast, zero-overt contrasts and bound-free contrasts occur regardless of the absolute frequency of the host: They are favoured by the RELATIVE frequency of one of the contrasting pairs. This is a very general form-frequency effect, which is found in many other contexts. Thus, we find singular/plural pairs such as house/houses (with high absolute frequency) and pairs such as hut/huts (with much lower absolute frequency). The zeroovert contrast is due to the consistently lower relative frequency of the plural. Likewise, we find alienability splits not only between high-frequency 'hand' and 'house', but also between low-frequency 'knee' and 'hut' (see §8 below for more discussion of absolute and relative frequency).
Thus, on closer inspection, the cumulative expression of possession does not favour Haiman's explanation, because it would predict that lower-frequency body-part terms such as 'ear' or 'knee', and lower-frequency kinship terms such as 'cousin' or 'greatgrandfather' should also occur in this pattern. In fact, however, it seems that it occurs only with very high-frequency kinship terms. But more research is needed on these kinds of patterns, as the few examples mentioned here do not give a conclusive picture.

A wrong prediction of the iconicity explanation: Middle position of the possessive marker
Since Haiman's iconicity explanation uses the notion of "distance", it predicts that the additional element in alienable constructions should occur in the middle between the possessor and the possessed noun. This is indeed what we find in many cases, e.g. in the canonical examples from Abun in (1) and Jeli in (4), and also in most of the examples in (6)-(12). By contrast, the predictability explanation says nothing about linear order, as it only concerns the presence or absence of additional coding material that signals the possessive relationship.
When we look at a wider range of languages with an alienability split, it turns out that the possessive marker is not constrained with respect to its position. It may occur to the left of both the possessor and the possessed noun, as seen in (24), or to the right of both the possessor and the possessed noun, as seen in (25). (See also the Tommo So Dogon example in (12)  'my hand' (Elbert 1974: 55, 61) (25) a. O'odham ñ-mi:stol-ga ñ-je'e (Uto-Aztecan) 1SG-cat-POSSD 1SG-mother 'my cat' 'my mother' (Zepeda 1983) b. Koyukon se-tel-e' se-tlee' (Athabaskan) 1SG-socks-POSSD 1SG-head 'my socks' 'my head' (Thompson 1996: 654, 667) c. Achagua nu-caarru-ni nu-wíta (Arawakan) 1SG-car-POSSD 1SG-head 'my car' 'my head' (Wilson 1992) Thus, these data are consistent with the predictability explanation, but they are not expected on the iconicity explanation. Haiman (1983: 795) himself cites the Puluwat example (24) and recognizes that it is a problem for his explanation in terms of iconicity: "Clearly, the classifier is not interposed between possessor and possessum. It is possible that, at some earlier stage of the language, the possessive affixes also followed alienably possessed nouns... Word order could change in defiance of iconicity. Perhaps, then, it will be necessary to revise [my earlier statement in terms of distance]..., by claiming the following: (37) In no language will the phonological expression of inalienable possession be bulkier than that of alienable possession.
Whether this revision is necessary depends on the frequency of the pattern exemplified by Puluwat." Even thirty years after Haiman's paper, there are no systematic cross-linguistic data on the cross-linguistic frequencies of the various patterns. However, it is clear that the patterns in (24) and (25) are consistent with Universal 1 and the predictability explanation, but do not follow from the iconicity explanation.

Predictions not made by the iconicity explanation
In addition to phenomena where both the iconicity and the predictability explanations make predictions about the form of adpossessive constructions with possessed-noun splits, there are also phenomena where the iconicity-of-distance explanation makes no predictions but the predictability explanation leads us to certain expectations. These concern the length of the possessive marker ( §6.1), as well as situations in which an adpossessive construction is obligatory ( §6.3) or is not possible at all with certain kinds of nouns ( §6.2).

Length of the possessive person forms
In addition to the observation that inalienable constructions tend to be zero-coded, we can also observe that the possessive person forms tend to be shorter in the inalienable construction (cf. Nichols 1988: 564). 6 (26) Universal 3: If a language has an adnominal alienability split, and one of the constructions is coded with shorter person forms while the other is coded with longer person forms, it is always the inalienable construction that has the shorter person forms, while the alienable construction has the longer person forms.
This universal is similar Haiman's statement in his (37) (as just seen in the quotation in §5).
In the examples in (20a-d), the possessive person forms are shorter in the inalienable construction. 7 We saw that the length of the forms seems to be a factor in their bound vs. free status. But length distinctions also occur when both types of person forms are free (judging by the orthography), or both are bound: (27)  Just as the zero vs. overt contrasts are predicted by the predictability explanation, the short vs. long contrast is also predicted by it. By contrast, there is no difference in distance here, so the iconicity explanation makes no prediction.

Impossessible nouns
Some languages have some nouns that cannot occur as possessed nouns in a possessive construction, e.g. in Yucatec Maya (Lehmann 1998: 57-58), where the nouns in (28) are among those that cannot occur with prefixed possessive person forms. set of nouns. There were some languages for which there was no apparent difference ... but there were no languages which reversed this tendency and used a longer or more complex marker for 'inalienably' possessed nouns" (cf. also Nichols 1988: 575). 7 The length distinction is only found with person forms, not with full nominals. I am not aware of any language which shortens its full-nominal adpossessor (something like "father's house" vs. "fa's brother"). This is probably because person forms tend to be short and idiosyncratic anyway, with a lot of cumulative and suppletive forms. 8 The Hungarian facts are discussed in a typological context by Ortmann & Gerland (2014 Such nouns are called IMPOSSESSIBLE NOUNS ("not possessable") by Lehmann. The phenomenon was also noted by Nichols & Bickel (2005a). That these nouns cannot occur in a possessive construction finds a natural account in my predictability-based explanation. Natural phenomena like 'sky' or 'world', and nonrelational person nouns such as 'woman' occur very rarely as possessed nouns in languages that allow such constructions. Thus, while English allows your woman or Kim's sky, such expressions are rare because they need a very special construal. As Lehmann (1998) puts it, person nouns and environmental nouns are "highly unfit as possessa", and it can easily be seen in any corpus (e.g. of English) that nouns such as 'sky' or 'woman' occur very rarely as possessed nouns.
Thus, in order to convey the idea that a 'woman' or a 'wind' is possessed, speakers of some languages need to make a greater coding effort. In Yucatec Maya, the ordinary prefixing construction does not allow such nouns, but this does not necessarily mean that an English phrase such as your woman cannot be translated into Yucatec. What speakers of this language probably have to do is resort to a more complex paraphrase, perhaps a relative clause construction ('the woman that belongs to you'), or an appositive noun that can be possessed ('the woman your-possession'). 9 The relationship between ordinary possessive constructions and such roundabout expressions would not normally be called a "coding split", because only one of the two expression types is a special grammatical construction. But in terms of coding length, there is no difference: the relationship between 'woman that belongs to you' and 'your house' in Yucatec Maya is analogous to the relationship between 'my garden' and 'my arm' in Abun. There is no need in this approach to make a strict distinction between grammatical constructions and "roundabout expressions".
To make the parallel between the alienability split and the split as discussed here even clearer, we might set up an implicational scale as in (29), where the term SUPER-ALIENABLE refers to the semantic group of nouns (environmental phenomena, wild animals, nonrelational person nouns) which very rarely occur in a possessive construction, and which correspond to a language-specific class of impossessible nouns in some languages.
(29) inalienable nouns -alienable nouns -super-alienable nouns Universals 1-3 could be reformulated in such a way as to cover not only the two noun types on the left-hand side, but all three types. It appears that in this stronger formulation, they would still be valid (see §7 below).
Thus, while rare occurrence in texts generally leads to a requirement of greater length of coding, it may also sometimes result in complete lack of grammatical coding (cf. Haspelmath 2008b: 189-190).

Possidend nouns (= obligatorily possessed nouns)
In a fair number of languages in different parts of the world, some nouns must occur as possessed nouns in possessive constructions. They cannot (normally) occcur in an unpossessed, absolute way. For example, in Koyukon (an Athabaskan language of Alaska), the word for 'my head' is se-tlee', but one cannot simply say *tlee' for 'head' (Thompson 1996). Such nouns are thus the opposite of the impossessible type of §6.2, and I call them POSSIDEND NOUNS. 10 These nouns are typically body-part terms or kinship terms, i.e.
inalienable nouns in the sense of §2. 11 Even though this phenomenon is quite well-known, and not unexpected on the traditional view that the alienable/inalienable distinction is primarily due to the fact that some nouns are inherently relational, the question to what extent a possessive construction obligatorily requires a possessor is rarely studied thoroughly.
The most extensive study of phenomena of this kind is Nichols & Bickel (2005a), who examine languages with "obligatory possessive inflection". The phenomenon of a possidend class of nouns is discussed in the literature almost exclusively for nouns in which the possessor occurs as a bound person index on the noun, so Nichols & Bickel do not distinguish between nouns with obligatory possessive inflection and nouns with an obligatory free possessor. 12 We can distinguish two subtypes of possidend nouns, depending on what happens when speakers exceptionally want to talk about the relevant referent in an absolute sense, i.e. without a possessor. I discuss these in §6.3.1 and §6.3.2, before providing an explanation of the observed generalizations in §6.3.3.

Absoluble possidend nouns
The first subtype of possidend nouns is called ABSOLUBLE (following Lehmann 1998: 51), because they can be "absolutized" by an additional marker which indicates that the noun is not possessed. This kind of marker is called ANTIPOSSESSIVE MARKER here, following Stiebels (2006: 181) (with gloss abbreviation APOSS). 13 Four examples are given in (30).
10 Latin nomina possidenda 'nouns that must be possessed' (using the Latin gerundive form ending in -endof the verb possideo 'possess'). 11 Nichols (1988: 564) and Nichols & Bickel (2005a: 238) call these nouns "bound nouns". 12 We rarely read about cases like Old Georgian, where possessors are said to be required for kinship terms even though they are not bound person markers (Khizanishvili 2006). However, there is no reason to think that such languages are rare (Dahl & Koptjevskaja-Tamm (2001) also mention Sirionó and Guaraní). 13 Lehmann's term for a marker of this kind is derelationalizer, and Ultan (1978: 27) called it an alienizer. Graczyk (2007: 53) uses depossessivizier. A reviewer suggests that markers of this kind seem to be derivational rather than inflectional, in contrast to genitive marking for possession. I am not sure how one could show this (because the distinguishing criteria are notoriously problematic), but in my approach, the difference between inflection and derivation plays no role. Terms like marker and coding are neutral between these two (putative) types of marking, just as they are neutral between (what is often called) morphological/synthetic and syntactic/analytic marking. 'his eye' 'eye' (Seiler 1983: 25) We can thus say that there is a general tendency for inalienable nouns (kinship terms and body-part terms) to require a special marker in non-possessed contexts. This is formulated as Universal 4, which is very similar to Universal 1 but concerns coding in non-possessed contexts.
(31) Universal 4: If a language treats alienable and inalienable nouns differently in non-possessed contexts, and one of the constructions is overtly coded while the other one is zerocoded, it is always the alienable nouns that show zero-coding, while the inalienable nouns show overt coding (by an antipossessive marker).

Inabsoluble possidend nouns
In addition to absoluble possidend nouns, there are also what Lehmann (1998: 52) calls INABSOLUBLE nouns, i.e. nouns which cannot be used outside of a possessive construction at all, not even with an antipossessive marker. Lehmann's discussion concerns Yucatec Maya, which has both kinds of nouns among its class of inalienables. Some examples of inabsoluble nouns are given in (32).
Here we have the opposite of the impossessible nouns of §6.2: Nouns that must be possessed, and where there is no grammatical construction that allows speakers to use them in an absolute sense. 14 However, again there are ways in which speakers could get around this grammatical restriction. Thus, Yucatec Maya speakers could presumably say 'someone's face' or 'the root of something' in order to talk about a face or a root without mentioning a specific possessor. This would not normally be called an antipossessive construction, because it is not a special grammatical construction at all. But fundamentally, there is again no difference: the relationship between 'someone's face' and 'my face' in Yucatec Maya is analogous to the relationship between k'e-tlee' 'head' and se-tlee' 'my head' in Koyukon.

Explanation
Iconicity of distance does not make any predictions about unpossessed constructions, but the predictability-based perspective again provides an explanation: When a noun occurs in a possessive construction very frequently, it may end up occurring obligatorily in this construction, and when it is to be used in an absolute way, without a possessor, it may be necessary to add special antipossessive marking to counter the strong expectation that a possessor will be found.
It is true that the phenomenon of possidend nouns is also expected on the view that grammars tend to exhibit form-meaning correspondences. Since the possessor seems to be notionally necessary with inalienable nouns, 15 it is not surprising that it should be syntactically obligatory in some languages, any more than it is surprising that subjects and objects are syntactically obligatory with transitive verbs in many languages (cf. Lehmann (1983: §3.2-3.3) for a particularly clear statement of the relation between coding and semantic relationality, both in verbs and in nouns; Stiebels (2006) is a more recent paper in the same spirit). But the phenomenon of antipossessive markers ( §6.3.1) is not expected on semantic grounds, because no meaning is added by these markers. 16 Creissels (2006: 157-158) says that "one can speak of iconicity, because the longer form of the noun is also more complex semantically in the sense that it implies the cancellation of a feature inherent to the noun's meaning". 17 Whether meanings that lack a feature can 14 On the analogy of the "super-alienable" noun meanings of §6.2, one might expect that there is also a group of "super-inalienable" noun meanings which tend to be possidend and inabsoluble. I am not aware of evidence that there is any semantic coherence to the inabsoluble nouns, so it is unclear whether this expectation is borne out. 15 The claim that kinship terms and body-part nouns are necessarily possessed sounds plausible and is often made, but in fact, artifact nouns such as 'house' or 'knife' are difficult to imagine without a human possessor as well. Nevertheless, languages typically treat artifact nouns just as they treat nouns such as 'cat' or 'nut'. Thus, to what extent the meaning of possession is really "inherent" in kinship and body-part term is still open to discussion. 16 In a few languages, nouns with antipossessive markers can take possessive indexes in addition, resulting in a semantic contrast, as reported for Navajo by Young & Morgan (1987: 3) (and cited by Nichols & Bickel (2005a: 238): bi-be' 'her milk (from her own breasts)', 'a-be' 'something's milk', be-'a-be' 'her (store-bought) milk'. For the contrast between bi-be' and be-'a-be' one could invoke Haiman's iconicity of distance, because there is a formal distance in the second form that can be seen as corresponding to a semantic distance. But on Haiman's account, it is puzzling that there also exists a form 'a-be', without the possessive prefix. 17 "On peut parler d'iconicité, puisque la forme la plus longue du nom est aussi plus complexe sémantiquement au sens où elle implique l'annulation d'un trait inhérent au signifié du nom." be regarded as "more complex" is a matter that I would like to leave to semanticists, but I fear that if one is too liberal in one's definition of semantic complexity, one might end up saying that any meaning that is (rare and hence) unexpected is semantically complex.

Summary of proposed universals
We can summarize the universal trends that we have hypothesized so far as in Universal 5 (for adpossessive constructions) and Universal 6 (for nonpossessed occurrences of nouns).
Inalienable nouns (kinship terms and body-part terms) and alienable nouns thus behave in a mirror-image way. This cannot be easily seen in individual languages, and some of the relevant patterns are not very frequent, but they nevertheless seem to be robust crosslinguistic trends. Note that Universals 5-6 are formulated as tendencies rather than absolute universals, because they generalize over the various subtypes. The difference between absolute universals and universal tendencies is not really relevant in the current context, because my explanation does not predict absolute impossibility of the dispreferred patterns (however, I have encountered very few counterexamples). A still more general formulation of the trends is possible if we return to the scale in (28) above (repeated here), which distinguishes three broad semantic groups: inalienable, alienable and super-alienable nouns. We can call this scale the POSSESSOR-PROMINENCE SCALE.
(29) The possessor-prominence scale: inalienable nouns -alienable nouns -super-alienable nouns On the basis of this scale, we can formulate the hypothetical generalization in (35), which subsumes all the other universals seen so far: (35) Universal 7: The further to the left on the possessor-prominence scale a noun is located, the shorter (and hence more bound) is the marking of the possessive construction, and the longer (and hence less bound) is the marking of the nonpossessed occurrence. Conversely, the further to the right on the possessor-prominence scale a noun is located, the longer is the marking of the possessive construction, and the shorter the marking of the nonpossessed occurrence.
Here zero coding, short coding, bound coding and obligatoriness are subsumed under "shortness (and hence boundness)", because zero coding is simply the extreme case of shortness, and obligatoriness simply means that a longer (and more roundabout) expression has to be used if the relevant meaning is to be conveyed (assuming that if given enough time, speakers can express every meaning in every language). 18 As noted in Haspelmath (2008b), such mirror-image generalizations are characteristic of a wide range of oppositions in grammar, and they all seem to be due to frequencyinduced predictability, following the causal chain in (16).

Relative and absolute frequencies
We saw above ( §3.3) that inalienable nouns occur more often as possessed nouns in possessive constructions than alienable nouns. This was the basis for my explanation of the coding differences: The percentage of possessed occurrences is significantly higher in one group than in the other, i.e. the relative frequencies of possessed occurrences differ in the two groups.
However, some authors have related formal properties of grammatical constructions to absolute frequencies rather than relative frequencies, so the differences between these two kinds of frequency needs to be discussed briefly here.
Perhaps most notably, Croft (2008) argues that coding asymmetries should be explained in terms of absolute frequency: "an economy explanation only works if one uses relative frequency of unpossessed vs. possessed inalienable nouns compared to the relative frequency of unpossessed vs. possessed alienable nouns. But all other examples of typological markedness -frequency-based differences in the structural expression of concepts -are of absolute frequency, not relative frequency. Many such examples are given in Greenberg (1966) and Bybee (1985); see also Croft (2003: 151, 154)." (Croft 2008: 51) This is a surprising statement, because all the examples of frequency differences between contrasting categories in Greenberg (1966) (the seminal study that inspired my research on form-frequency correspondences) consider relative frequency, not absolute frequency. For example, Greenberg observes that in general, singulars are more frequent than plurals, and plurals in turn are more frequent than duals. But this is true only in relative terms: For example, the dual of a high-frequency word such as 'friend' ('two friends') will be more frequent than the plural of a lower-frequency word such as 'witch' ('witches'), and it will even be more frequent than the singular of a lowest-frequency word such as 'nonagenarian'. In all these words, the relative frequencies are in accordance with the general trends, and the differences in absolute frequencies are irrelevant for the coding of singular, plural and dual. Croft's statement thus seems to be based on a confusion, but he gives a reason for the expectation that absolute frequency rather than relative frequency should be the relevant type of frequency to explain "economic coding": 19 18 A reviewer notes that an even shorter version of Universal 7 would be: "The marking length of an adpossessive construction used with a type of noun correlates inversely with the likelihood of the presence of a possessor on this type of noun." 19 Note that Haspelmath (2008a) used the term "economic motivation", based on Haiman (1983), for what is called "predictability explanation" in this paper. Thus, Croft's "economy effects" are what are called "predictability effects" here.
"It is not an accident that absolute frequency has been found to be the causal factor for economically motivated linguistic patterns. The theoretical explanation for economy (e.g. Bybee 1985) requires absolute frequency. Economy effects are due to degree of entrenchment of linguistic forms (morphological forms or constructions such as the possessive) in the mental representation of linguistic knowledge. Entrenchment leads to routinization of the production of the form by a speaker, which in turn brings about reduction of that form. But entrenchment is a result of exposure to the number of tokens of the linguistic form; that is, entrenchment is a function of the absolute frequencies of forms, not relative frequencies." (Croft 2008: 52) It is true that Bybee's work on degree of entrenchment has been influential and is certainly important in many areas of grammar (see also Diessel & Hilpert 2015), but it is a misunderstanding to try to reduce form-frequency correspondences to entrenchment and absolute frequency. Entrenchment or absolute frequency is responsible for a variety of effects, most notably the preservation of irregularities and suppletion (as already noted above in §4.3). 20 However, form-frequency correspondences of the type described in §3.3 result from the higher predictability of the more frequent forms, and it is relative frequency that is relevant here. Reduction of form is not due to routinization, but to the possibility of giving less information to the hearer due to the higher predictability. (See also Hollmann & Siewierska (2007: §4) for fairly detailed discussion of relative and absolute frequencies in adpossessive constructions in English.)

The diachronic creation of alienability contrasts
As noted by Bybee (1988), functional-adaptive explanations need a diachronic component: Since the current language system is rigidly conventional, the adaptive forces must have been active in earlier diachronic change. Thus, to complete the picture, I will make a few remarks on ways in which alienability splits arise diachronically, and on how the different frequencies and thus the different predictability leads to the coding differences. (See now also van Rijn 2016b for a more detailed study of some of the relevant developments.) In general, there are at least two ways in which the higher frequency and greater frequency of one pattern leads to shorter coding (cf. also Haspelmath 2008b): (i) differential phonological reduction in the more frequent pattern (due to the Reducing Effect of frequency, cf. Bybee 2007), and (ii) differential inhibition of a novel construction type (due to what I call the Expectation-generating Effect).

Differential phonological reduction
Reduction is the mechanism that Zipf (1935) proposed to explain the frequency effects in lexical items that he observed. There seem to be widely available processes of shortening when an expression becomes more frequent. Zipf mentioned clipping (e.g. German Auto from Automobil), but there is also differential sound change, leading to greater reduction in frequent forms (e.g. Mańczak 1980). In (36)-(38), we see three examples of cases where a shorter inalienable pattern arose by phononological reduction from a fuller pattern, while the corresponding alienable pattern does not show the same reduction.
(36) Old Italian < Latin (Rohlfs 1949(Rohlfs -1954 Khizanishvili (2006) for discussion). It is true that the possessive pronoun itself was not reduced, and the loss of the internal inflection (deda-s čem-s [mother-DAT my-DAT] > deda-čem-s) may not have been purely phonetic, but this is a case of differential reduction, not inhibition as in the cases cited in the next subsection.

Differential inhibition of an expanding construction
Even though Zipf's explanation of form-frequency correspondence phenomena would lead us to expect otherwise, most cases of asymmetric coding are clearly not due to differential phonological reduction, but to differential inhibition of a new, more complex construction. Such novel constructions typically make an existing meaning more transparent or salient by including a special additional morpheme, and they are introduced when speakers want to call special attention to the relevant meaning ("extravagance", Haspelmath 1999). The novel construction may then expand and become more frequent in an increasing number of new contexts, but it will be prevented from spreading to the contexts in which the relevant meanings occur most often. 21 Consider the example of Maltese possessive constructions (cf. Koptjevskaja-Tamm 1996). Like many other modern Arabic vernaculars, Maltese has an alienability split (described in detail in Stolz et al. 2008 The novel construction arose from an appositive construction of the type al-kitaab mataaʕ-ii, literally 'the-book my-possession', which is a typical grammaticalization of a content word that makes an existing meaning more transparent, or expresses it more "extravagantly". But this novel construction did not expand to inalienable nouns: Maltese does not allow *l-id tiegħ-i 'my hand' (Koptjevskaja-Tamm 1996). Inalienable nouns still use the old pattern with a person suffix and with no special possessive morpheme. Synchronically, Maltese is thus just like the languages in (6)-(12), and it is quite possible that some of these have the same kind of diachronic origin. 22 The same kind of development can be observed in the history of Egyptian-Coptic, as described in detail in Kammerzell (2000) and Haspelmath (2015). The oldest attested stage of Egyptian had a productive pattern of direct possessive marking, by postposed possessive person forms or juxtaposed possessors. This pattern survived into Coptic only with a few body-part terms, e.g. rô-f 'his mouth', or hêt-s 'her womb'. With alienable nouns, the language resorts to a new possessive construction, involving a preceding definite article, e.g. pe-f-êi [ART-3SG.M-house] 'his house', pe-s-čoeis [ART-3SG.F-lord] 'her lord' (this interesting change was also noted by Creissels 2006: 155).
A third example is the Old French contrast between the old Inflected Genitive construction (e.g. li filz Deu 'God's son') and the new Prepositional Genitive with de (e.g. le duch de Bretagne 'the Duke of Brittany') (see Herslund 1980, among many others). While there are a number of factors that determine the choice between the old and the new construction, kinship and body-part terms are particularly prominent determinants of the old construction in Old French.
I hypothesize that the expansion of the new (and typically longer) construction is inhibited by the Expectation-generating effect of usage frequency: the expression of the possessive meaning is redundant when it highly expected on the basis of learned frequency distributions that there will be a possessor. Dahl & Koptjevskaja-Tamm (1998) make the strong claim that differential expansion is the only way in which an inalienability split can arise: "We suggest the generalization that an expanding possessive construction must encroach on the territory of pronominal possession for an alienability split to arise." However, the examples in (36)-(38) show attested cases of differential phonological reduction, so this statement seems to be too strong.

Conclusion
I conclude that a range of cross-linguistically recurring properties of inalienable and alienable adnominal possessive constructions can be explained by the fact that inalienable nouns occur more frequently as possessed nouns than alienable nouns. Alienability splits in adpossessive constructions can thus be subsumed under the highly general formfrequency correspondence principle of Haspelmath et al. (2014). Haiman's (1983) well-known iconicity explanation is less general than my explanation and makes some wrong predictions, so it should be abandoned.
More generally, it seems that the explanatory power of iconicity has been overestimated. For instance, all "iconicity of markedness matching" effects can be explained by frequency asymmetries as well (Haspelmath 2006: 40;. Linguists have a natural tendency to explain formal patterns semantically, but this is not the only explanation. Language structure not only reflects meaning, but also the pragmatic use that speakers make of language. Countering the hearers' expectations is a major pragmatic function of language, so it is not surprising that it should be reflected in grammatical structure as well. A cognitive-functional approach that is not usage-based and corpusbased (such as much of the classical functionalist work of the 1970s and 1980s) may go seriously wrong.
Of course, for a complete understanding of the coding asymmetries that we observe in grammar, we will ultimately need an understanding of the frequency asymmetries, not just of their effects. But it is not true that "frequency distributions ... do not provide an explanation because the frequency distributions themselves need to be explained" (Downing & Stiebels 2012: 425; see also Rainer et al. 2014: 17). Even if we had no explanation of the frequency distributions, they would still account for predictability and thus for shorter coding. However, in the case of adpossessive constructions, this is not a burning issue, because it is easy to understand why 'hand' should occur more often as a possessed noun than 'house'. Thus, I will not discuss this matter further here and trust that at least in the case of alienability splits, even skeptics will be convinced.