The English Possessive Marker in a Framework of Relevance

English nominals constructed with the morpheme {-s} as a so-called possessive marker may be assigned an indefi nitely large number of interpretations depending on the context of utterance. This raises interesting questions concerning the interface between semantics and pragmatics, most obviously concerning the more specifi c nature of the contextually invariable encoded content of the morpheme as well as the contribution made by that content to the process of comprehension. This article aims briefl y to suggest one solution to these problems by proposing an underdetermined procedural semantics feeding into a principled cognitive process of inference as proposed within the framework of relevance theory.


Aims
This paper is going to address the issue of the meaning of the {-s} morpheme in possessive constructions in English within the general framework of relevance theory (Sperber/Wilson 1986/1995. By possessive constructions I mean what is more traditionally referred to as the genitive 1 , for present purposes encompassing primarily the distributional patterns Taylor (1996)  Moreover, I will be concerned with the distinction between in particular the prenominal possessive and the competing postnominal of-construction, as in e.g. the boy's mother / the mother of the boy and John's bike / *the bike of John. My aim is basically to seek a unifi ed account of the encoded content of the {-s} morpheme -or possessive 2 marker, as I will also refer to it -in all its potential environments, one which may provide an adequate basis on which to explain the occurrence of what seems to be an indefinite number of meanings attributable to nominals in which {-s} occurs. My proposal as to the semantics of the possessive marker is thus intended to unite pragmatically determined representations within an inference-based interpretive framework, viz. relevance theory.

The problem
Why should the possessive marker be worth bothering with at all? From a meaning-based perspective possessive constructions are interesting largely because of the indeterminate number of interpretations to which they seem to be amenable. A simple nominal such as Peter's shirt might on the face of it refer to the shirt owned by Peter, the shirt worn by Peter, the shirt Peter designed, the shirt he painted, or photographed, or has stolen, or written about, or whatever. Clearly, the possessive morpheme is either exceedingly polysemous, or else the encoded content it brings with it into the nominal is suffi ciently abstract as to be compatible with a very wide range of meanings indeed. As such, we appear to be dealing with a phenomenon eminently suited to enquiry into the semantics/pragmatics interface; the data will point either to a wholly semantic account or to some division of labour between semantics and pragmatics.
Thus, if we contend that in a given context (1) below is assigned the interpretation in (2), to what extent is (2) then attributable to the encoded semantics of {-s}? And in the event that the contribution of that encoded content is only partial with respect to a relevant semantic cate-gory such as SOURCE (cf. Peter is the source of the 'shirt'), how does the hearer then arrive at the interpretation in (2)? (1) Peter's shirt is horrendous.
(2) The canvas Peter has painted and which portrays a shirt is horrendous.
The task here, then, is fi rst to propose a semantics for {-s}, and then to suggest in what way that semantics is signifi cant in the process of utterance interpretation.

Theoretical coordinates
Intuitively, it would make good sense to strive for a unitary account of the possessive morpheme covering the entire range of constructiontypes in which it occurs. In the interests of descriptive parsimony alone such an account would certainly be preferable. In general, I adhere to the methodological principle known as Modifi ed Occam's Razor, a meta-theoretical principle of economy put forward by Grice which states that "Senses are not to be multiplied beyond necessity" (Grice 1989: 47). As Carston (2002: 184-185) puts it, this: entails that, instead of positing a linguistic ambiguity to account for multiple interpretations of a linguistic expression, pragmatic principles and inferences, which are independently motivated, should be employed, wherever possible.
While this in itself calls for neat description, there are other reasons for preferring an account minimising the role of encoded semantics. Any assumption of cognitive economy in the comprehension process would seem to run against a polysemous account whereby the possessive marker is construed as encoding multiple meanings across a wide semantic fi eld. To the extent that the human mind is geared to minimising the cognitive effort expended in the interpretation of ostensive stimuli -as argued by relevance theorists -it would seem likely that human language is structured in such a way as to accommodate or refl ect that state-of-affairs. 3 I assume that the general idea that linguistically encoded meaning underdetermines 'what is meant' (to use Grice's term) is uncontroversial, and that the idea that the semantic entry for the morpheme should list all such highly specifi c conceptual senses as might occur at any time in any instance of discourse consequently may be dismissed. More contestable is the notion that encoded content underdetermines the proposition expressed, i.e. the explicit content of the utterance, or 'what is said'. This idea is forcibly presented in relevance theory, particularly in the work of Robyn Carston, who refers to the claim as simply 'the underdeterminacy thesis' (Carston 2002: 19). Recent work in the emerging fi eld of lexical pragmatics has shown that even the encoded content of conceptually fat lexical items, 'content' words, would appear to be underdetermined with respect to their explicit meaning (Wilson/Sperber 2004).
A monosemous account, then, seems favoured by (i) the assumption that the cognitive architecture favours simplicity insofar as processing of linguistic input operates on underdetermined rather than conceptually full-fl edged representations; (ii) the assumption that the interpretive system is architecturally geared to minimising effort; (iii) Modifi ed Occam's Razor, the general methodological principle of descriptive economy. Further, if we accept a distinction between procedural and conceptual semantic content (see Blakemore 2006), we can suppose that procedural content at least will be fairly unambiguous. To the extent that {-s} is procedural, as I will presently claim, this would clearly further reinforce a monosemous approach.
If, then, we are to suppose that {-s} encodes an unambiguous and underdetermined semantics, this means that we have need of some theory of verbal comprehension that will allow us to account for how, exactly, the hearer of, say, (1) arrives at an interpretation such as (2). This brings us into the domain of pragmatics. I have already noted that relevance theorists fundamentally reject notions of communication relying exclusively on processes of encoding and subsequent decoding of more or less specifi ed semantic content (see Sperber/Wilson 1986/1995. Instead, human communication generally is construed as essentially inferential. That is, in the case of verbal communication, utterances are taken to encode a schematic semantics which is decoded automatically by a linguistic input module resulting in the hearer representing a socalled logical form. This is a blueprint requiring inferential manipula-tion in order for the hearer to be able to construct a representation of the speaker's informative intention, i.e. what it was she intended to convey. The goal of an inferential pragmatics is thus "to explain how the hearer infers the speaker's meaning on the basis of the evidence provided" (Wilson/Sperber 2004).
The account of utterance interpretation provided by relevance theory is grounded in "a general claim about cognitive design, the claim that human cognition is geared towards the maximisation of relevance" (Carston/Powell 2006). Relevance itself is seen as a potential property of input to inferential processing. More specifi cally it is a matter of 'cognitive effects'. An input may deliver cognitive effects by yielding new assumptions, or by providing evidence that strengthens, contradicts or eliminates existing assumptions held by the hearer. Relevance is a trade-off relation between processing effort on the one hand and cognitive effects on the other: an assumption is deemed optimally relevant to the extent that it provides maximum cognitive effect for a minimum of processing effort. Central to the theory is the communicative Principle of Relevance (Sperber/Wilson 1986/1995 (3) Communicative Principle of Relevance Every ostensive stimulus conveys a presumption of its own optimal relevance.
Any ostensive utterance thereby conveys as part of its encoded content the assumption that it is optimally relevant to the hearer, i.e. that processing it will yield a maximum of cognitive effects. What all this means is that the process of interpretation, far from being a haphazard, hit-or-miss kind of activity, is in fact highly principled. It proceeds thus (Carston/Powell 2006): [The principle of relevance] licenses the hearer to consider possible interpretations in order of their accessibility (that is, to follow a path of least effort) and to stop as soon as he reaches one that satisfi es his expectation of relevance.
My claim here is that the problem of accounting for the relationship between the context-invariable encoded semantics of {-s} and contextually assigned meanings associated with nominals in which it occurs can be solved within a relevance-based framework.

The semantics of {-s}
Nominals constructed according to the possessive schema ((N1-s) N2) have been variously construed in terms of meanings such as possession (Peter's new car), kinship (Paul's sister), and part-whole relation (Mary's nose), to name but three. Often, the concept of possession is extended so as to provide a broad frame of semantic reference with which to associate the meaning of the possessive marker. Clearly, such conceptual categories are less descriptive of {-s} than they are of the nominals in which {-s} occurs. Equally, if we are to say simply that {-s} encodes possession in some very broad sense, we need to specify exactly what we mean by that concept. As it stands, it would seem merely to be a convenient label for something much more abstract and much less expressable. Taylor (1996) contends that construing the semantics of {-s} simply in terms of 'abstract relation' is less than satisfactory. Partly because he sees 'possession' as being a default reading of any nominal token involving {-s}, and partly because such a meaning would fail to account for some distributional constraints on the occurrence of {-s}, for example: The reference-point model is simply the idea that we commonly invoke the conception of one entity for the purposes of establishing mental contact with another. Taylor (1996) elaborates slightly on Langacker's proposal, suggesting (1996: 17) that: in opting to use a possessive expression, the speaker is instructing the hearer on how best to identify the referent that he, the speaker, intends. The speaker, that is, invites the hearer to fi rst conceptualize ('establish mental contact with') the one entity […] with the guarantee that this will facilitate identifi cation of the target entity.
In the main, I concur with a reference-point analysis insofar as I consider {-s} to encode procedural information directing inferential manipulation of conceptual content towards a relevant representation. Specifi cally, {-s} instructs the hearer to represent N2* (i.e. the concept expressed by the nominal N2) as part of world N1*, where world N1* is the set of contextual assumptions stored at the conceptual address activated by the nominal N1. For instance, in a simple nominal like (8): (8) that man's wife the noun phrase that man (N1) activates a concept THAT MAN (N1*) that provides a context of associated assumptions (world N1*), retrieved from the conceptual address or else constructed ad hoc. At the same time, the possessive marker {-s} encourages the hearer to represent the concept WIFE (N2*) activated by the noun wife (N2) as part of that set of assumptions (world N1*). This means that assigning reference to (8) is dependent on resolution of the kind of relationship that is predicated to exist between the two entities, this being a pragmatic process of relevance-driven inferential computing in context. The semantics of {-s} is thereby procedural, rather than conceptual in nature insofar as it is an instruction to the hearer as to how the conceptual content of the nominal is to be cognitively manipulated. The possessive marker does not merely encourage the hearer to represent some notion of 'unspecifi ed abstract relation'; rather, it encodes a specifi c instruction to integrate one concept within the set of assumptions associated with a second concept. This is a unidirectional operation, and as such it refl ects the non-interchangeable sequential nature of examples like (4) and (5) above.
Note that the notion of a procedural semantics is on the face of it fully compatible with a framework such as instructional semantics. Where instructional semantics and relevance-based pragmatics diverge, however, resides in the fact that only relevance theory attempts to account for exactly how a procedural, or instructional, semantics contributes to cognitive processing of logical forms. While an instructional approach quite reasonably might assign the kind of semantic content to {-s} as is proposed here, a relevance-based account will further seek to explain in a principled manner exactly how that content inputs to a full-fl edged, cognitively relevant representation. The two approaches are hardly incompatible; they merely differ in terms of their explanatory scope.
In what way then does encoded content contribute to the representation of possessive-marked nominals in specifi c contexts of utterance?

Interpretation
Let us start by considering the concept of possession. As noted, Taylor (1996) considers some notion of possession to be a default reading of nominals involving {-s}. This is a claim that, in the absence of any obvious context, linguistic or otherwise, that would point to some other interpretation, a nominal like (9) below will be construed as meaning something like (10): Peter's car (10) the car Peter owns On the face of it, this seems reasonable. It is clearly the case, however, that if we replace car with some other noun, the possession reading becomes less obvious, as the simple example below illustrates: (11) Peter's absence Possession obviously has to be some much more abstract notion than our everyday understanding of the concept, so abstract in fact that it becomes tantamount to the wholly unspecifi ed relation that Taylor quite reasonably objects to. Moreover, while there is no reason to suppose that linguistic items cannot encode both procedural and conceptual content at the same time (see Nicolle 1998), it would seem to be an unnecessary "multiplication of senses", to use Grice's words, and thereby a contravention of Modifi ed Occam's Razor, to suggest that this is the case for {-s}. Not least because any 'possession' representation, in the more current sense, would seem clearly to be dependent on the kind of lexical environment in which {-s} occurs.
Thus, all things being equal, an utterance of (9) is likely to activate a series of assumptions about Peter, these being either retrieved from memory or else constructed ad hoc. Two such assumptions are quite conceivably (12) and (13): (12) Peter is an adult human. (13) Adult humans very often own cars.
Given (12), (13) is immediately accessible and therefore of low cost to processing. A simple relevance-driven process of non-demonstrative inference employing (12) and (13) as premises will yield as a socalled implicated conclusion an assumption to the effect that Peter's car means 'the car that Peter owns'. To the extent that this provides cognitive effect and is compatible with expectations about the speaker's informative intention, this will be a relevant interpretation and processing will stop. At no point do we need to postulate 'possession' as an encoded representation.
Indeed, my claim is that any specifi c meaning assigned to a nominal involving {-s} can be accounted for by positing the above semantics as input to inferential processing guided by principles of relevance. Another example: (14) the car's headlights Constructions like (14) tend to be assigned a partitive interpretation whereby the entity expressed by N2 is taken to be a part of the whole that is expressed by N1. Again, this is easily accounted for if we suppose that the encoded content of {-s} is as outlined above, and that the lexical items involved activate concepts whose encyclopaedic properties include assumptions like (15) and (16) Partitive readings are in such cases immediately accessible interpretations yielded by the same kind of inferential process as posited above for (9).
One obvious demand on the theory is that it should be able to account for well-attested distributional constraints such as those exemplifi ed below: Since the possessive marker instructs the hearer to integrate N2* into world N1*, the nominal occupying the N1-slot must be capable of fulfi lling that function. That is, it must exhibit certain properties. Collectively, we can refer to these in terms of cognitive utility. A nominal will possess cognitive utility value to the extent that it activates a cognitively salient concept, i.e. one that is easily accessible and relatively rich in terms of the kinds of encyclopaedic assumptions that may be accessed at its conceptual address or constructed online. We might expect cognitive utility to be closely linked to ontological categories, so that fi rstorder entities, for example, will tend to have greater utility value than second-order entities, and so on: Here, the relatively high salience of the fi rst-order entity expressed by Peter means that the possessive marker will readily attach to the noun, whereas the relatively low salience of the second-order entity expressed by laptop means that {-s} will attach less readily. Similarly, the thirdorder entity expressed by idea, which presumably has least salience, means that {-s} arguably is more likely to be rejected. We should note, however, that there are clear tendencies, especially in American English, towards a marked extension of the domain of the possessive marker, so that {-s} now increasingly attaches to nouns previously deemed less than amenable to such marking (see Rosenbach 2003). Moreover, salience should clearly not be regarded as an invariable property of entities. Rather, it is invested in them by cognitive subjects. So while a second-order entity might most immediately seem to be potentially less salient than a fi rst-order entity, it may nevertheless be invested with greater salience in the run of discourse. This allows for the attachment of {-s} to nouns which in terms of the ontological status of their denotations might appear less than amenable to possessive marking, as for example in (21) above. Hawkins (1981) has proposed a semantic hierarchy of sequential relations to account for the distributional relationship between {-s} and the competing postnominal of-construction:

(24) [HUMAN] < [HUMAN ATTRIBUTE]] < [NON-HUMAN ANIMATE] < [NON-HUMAN INANIMATE]
Here, the arrow indicates sequential precedence, so that human entities are taken to assume precedence over human attributes, and so on. The hierarchy accounts neatly for examples like the following: So, in (25) the two constructions alternate freely due to the equal standing of the two human entities in the hierarchy. By contrast, in (26) the postnominal of-construction is blocked due to Mary having sequential precedence over car. In (27) both constructions are again freely available due to the equal status of the non-human inanimate entities expressed by ship and funnel. Examples like the school's pupils, which ought to be excluded by the hierarchy, but which nevertheless certainly occur with signifi cant frequency, are explained in terms of social institutions, such as schools, which are essentially defi ned by their dependency on human activity, being cognitively invested with human properties whereby they advance, as it were, up the hierarchy. Hawkins' framework does not, however, account for the unacceptability of examples like (19a); in this particular case, both nouns denote non-human inanimate entities and as such ought to be freely interchangeable. Yet this is clearly not the case. Neither are we able to suggest that house is suffi ciently characterised by human activity as to allow {-s} attachment in the same way as school. Note also that school itself will also reject the possessive marker when collocated with a noun like roof. Obviously, the situation is more complex than Hawkins' proposal suggests, and it would seem that a full account should include not only the nature of N1, but also that of N2. This will not be part of my endeavour in the present article.
Hawkins' proposal equates with a notion of cognitive utility or 'topicworthiness' (Taylor 1996). It is descriptively useful insofar as it would seem to account fairly adequately for the relative distributional patterns of the two competing constructions. However, it does not provide any clear picture of the relative semantic status of the prenominal and postnominal possessive forms. Indeed, Hawkins suggests that the two forms are synonymous, both encoding some notion of 'intrinsic relation'. This may be less than satisfactory. The examples in (28), from Taylor (1996), are by no means necessarily co-referential: (28) a. Chomsky's students b. the students of Chomsky I suggest that, while the semantic content of {-s} instructs the hearer to integrate N2* into world N1*, the postnominal construction is semantically distinct. Thus, Tyler and Evans (2003), working within a framework of cognitive semantics, construe the encoded content of the preposition of in terms of an intrinsic relation between Trajector (TR) and Landmark (LM) entities. Adopting this proposal allows us to account for examples like (28). Thus, the nominal in the a-example instructs us to represent N2* as part of world N1*. We can reasonably assume that among the assumptions it is likely to immediately activate will be e.g. (29) and (30): (29) Chomsky is someone associated with students (e.g. a university professor).
That being so, it is but a short inferential step, given the principles of relevance, to an interpretation along the lines of (31): (31) the students taught by Chomsky Conversely, the b-example in (28) encourages the hearer to represent N1* as being intrinsic to N2*. Among the assumptions immediately activated we can expect to fi nd (32) and (33): (32) Students are intrinsic to Chomsky by virtue of Chomsky being insertable as an object in the schema (student STUDY x).
On this basis, a relevant interpretation will be (34): (34) the students of Chomsky's work Distinguishing between the semantic content of the two constructions also allows us to account for their co-occurrence in examples like (35), whose relevance rests on their being distinct from a related nominal such as (36).
(35) a friend of my mother's (36) a friend of my mother Following the proposals here, (35) would appear simultaneously to represent the friend as being intrinsically related to my mother and to identify some unspecifi ed entity with my mother. That the entity is unspecifi ed follows from the dissolution of the frame ((N1-s)) N2). In the absence of a specifi ed N2 slot, the most readily available candidate concept to associate with the speaker's mother, and the one most likely to yield relevance, will be that expressed in the immediate linguistic context by a friend.
Note that the contribution of {-s} is signifi cant. Thus, it is by no means given that (36), for example, 'means' the same as (35): Mrs Jones may well be a friend of my mother without necessarily being a friend of my mother's. That is, (35) strongly implies that my mother considers Mrs Jones to be one of her friends, whereas in (36) this is not conveyed. In more abstract terms, and with reference to the possessive schema ((N1-s) N2), the specifi c instruction to integrate N2* into world N1* picks out N1* as the salient concept in terms of which N2* is to be represented. This strongly encourages the assumption that my mother considers Mrs Jones to be her friend. In (36), however, N1* is not picked out in this way, rather the hearer is merely instructed to represent a friend as being intrinsic to my mother. This does not exclude a reading along the lines of (35). However, it does not explicitly encourage such an interpretation, so the assumption that my mother is not aware of Mrs. Jones being sympathetic to her remains available as a relevant interpretation.
Further constraints are apparent in the case of what Taylor (1996) refers to as possessive nominalisations, i.e. constructions with {-s} which involve deverbal nouns and which can be directly related to situational descriptions involving agent and patient roles. The nouns involved may be either 'cognitive nouns' or 'action nouns' (Taylor 1996), these giving rise to two distinct categories known as the knowledge paradigm (cf. example 37 below) and the destruction paradigm (example 38) (39) and (40) (39) and (40) pick out categories rather than category members, the marker here operates not on tokens but on types.
How does the hearer of (41) know that he is dealing with type rather than token? (41) Where are the children's books?
Leaving aside clues deriving from prosody, we can state rather obviously that (41), when uttered, will be contextually anchored in a specific situational location. Other things being equal, in a context in which specifi c tokens of the entity 'child' are salient, assumptions relating to those tokens will be potentially relevant to the interpretation of an utterance like (41). In a context in which the family is packing to go on holiday, a 'token' interpretation of (41) is likely to be relevant. However, even in this case, a 'type' interpretation remains available, the referent of the nominal in each case being identical. In the case of (41) being uttered by a potential customer in a bookshop, however, individual tokens have low salience, whereas the type is extremely salient. In a relevance perspective, the hearer simply searches for the most readily available contextual assumptions on the presumption that the utterance is optimally relevant and that an optimally relevant interpretation is one which maximises cognitive effect for a minimum of processing effort. The interpretation of (41) follows simply from the manipulation of semantic input and activated assumptions according to considerations of relevance.
Finally, let us very briefl y return to examples (6) and (7) above. We stated that these ran counter to any idea that {-s} merely predicates an unspecifi ed relation between entities. One explanation of their unacceptability (or at least their doubtful acceptability) is that N1* is not generally thought to be in any relation with N2* that might be justifi ed in terms of N2* being unidirectionally incorporated in world N1*. In other words, chips are more obviously a part of the world activated by the complex nominal fi sh and chips than of the world activated by fi sh alone. This would arguably make examples like ?the fi sh and chips' fi sh marginally more acceptable.

Concluding remarks
Above I have presented a claim about the more exact nature of the encoded content of the {-s} morpheme in English. This claim is founded on a distinction between an invariable underdetermined semantics and an inferential process of comprehension to which that semantics is contributes and which yields fuller conceptual representations of the meaning intended to be conveyed by the speaker.
While I am much in agreement with the fundamentals of Langacker's and Taylor's construal of the semantics of {-s} in terms of the reference-point thesis, and indeed with some of its more specifi c details, as I have just outlined, I do believe that relevance theory provides a potentially much more satisfactory framework than the cognitive grammar (CG) approach on which the aforementioned approaches are founded 5 . While CG rejects the notion of an autonomous syntax and does not operate with concepts like logic, propositions and truth-conditions, relevance theory (RT) accords such notions crucial importance in the comprehension process. It is my fi rm belief that understanding utterances is indeed a matter of logical inference based on the representation of truth-evaluable propositions derived from logical forms constructed on the basis of linguistic input.
More broadly, CG does not in any way account for how comprehension actually proceeds, whereas RT provides a holistic and principled explanation of the role of language as input to human communication. This article makes but a very small contribution to understanding how the possessive marker contributes to full-fl edged conceptual representations based on the idea of a schematic procedural semantics feeding into a relevance-driven process of inferential reasoning to yield famil-iar possessive meanings of the kind generally identifi ed in comprehensive grammars.