Describing derivational polysemy with XMG (2017)

Abstract: In this paper, we model and test the monosemy and polysemy approaches to derivational multiplicity of meaning, using Frame Semantics and XMG. In order to illustrate our claims and proposals, we use data from deverbal nominalizations with the suffix -al on verbs of change of possession (e.g. rental, disbursal). In our XMG implementation, we show that the underspecified meaning of affixes cannot always be reduced to a single unitary meaning and that the polysemy approach to multiplicity of meaning is more judicious compared to the monosemy approach. We also introduce constraints on the potential referents of derivatives. These constraints have the form of type constraints and specify which arguments in the frame of the verbal base are compatible with the referential argument of the derivative. The introduction of type constraints rules out certain readings because frame unification only succeeds if types are compatible.

## introduction a characteristic property of the outcomes of word formation processes is polysemy @xcite . in this paper, we model and test the monosemy and polysemy approaches to derivational multiplicity of meaning, using frame semantics and xmg. in order to illustrate our claims and proposals we use data from deverbal nominalizations with the suffix -al. following recent advance-ments in the study of the semantics of derived words in frame semantics @xcite , we focus on a well defined class of bases and examine attestations in context. in particular, in the present paper we examine -al nominals that are based on verbs of change of possession (e.g. rental, disbursal). what is a frame? a frame is a general format of mental representations of concepts which is also applicable to linguistic phenomena. it is a recursive attribute-value structure that provides information about a referent @xcite @xcite . word formation in frame semantics is generally treated in terms of referential shifts @xcite . for example, as we will see in the analysis, the suffix -al can target particular arguments of the base verb and shift reference from the original referent (i.e. causation event) to a new referent (e.g. theme). what is xmg? xmg (extensible metagrammar, @xcite ) is a modular and extensible tool used to generate various types of linguistic resources from an abstract and compact description. this description, the metagrammar, relies on the concepts of logic programming and constraints. xmg comes with a system of dimensions, allowing to separate the different levels of linguistic description (e.g. syntax and semantics), and providing dedicated languages adapted to the structures the user wishes to generate. in this work, the dimension we used is @xmath0, proposed in @xcite , where semantic frames can be described using typed feature structures descriptions. the rest of this paper is structured as follows: in section 2 we examine which readings are possible in context for -al nominals which are based on verbs of change of possession. we then provide a modeling of multiplicity of meaning using xmg. in section 3 we focus on monosemy approaches and in section 4 we offer a modeling of the polysemy approach. section 5 concludes the paper. ## -al on verbs of change of possession in this paper we focus on the suffix -al on verbs of "change of possession" @xcite . the class of verbs of change of possession comprises "give" verbs (e.g. give, rent), "contribute" verbs (e.g. submit, betroth), verbs of "future having" (e.g. promise, bequeath), verbs of "providing" (e.g. provide, redress), verbs of "obtaining" (e.g. retrieve, accrue), verbs of "exchange" (e.g. exchange, swap), and "berry" verbs (e.g. nest, clam). verbs of change of possession describe caused possession of the kind 'x causes y to have z', in which x is the agent, y is the recipient, and z is the theme @xcite @xcite . the general schema for verbs of change of possession in frame semantics is given in figure 1 in the form of an attribute-value matrix. in figure 1 , we model verbs of change of possession as causation events that involve three arguments; an agent, a theme, and a recipient. given that verbs of change of possession are causation events, they come with a bipartite structure that comprises a cause and an effect (for more on the modeling of events in frame semantics see @xcite . a typical causation event involves a relationship between situations and entities in which a particular entity (e.g. an agent) causes another entity (e.g. theme) to go from an initial situation to a result situation. in the case of verbs of change of possession, there is a start, i.e. an initial state, in which the agent is the possessor of the theme, and an end, i.e. a result state, in which the recipient is the possessor of the theme. as captured by the constraint "6 = 7", the initial state and the result state are not equal (plag et al., forthcoming). the suffix -al on verbs of change of possession derives event, result, and inanimate theme noun readings. consider the following examples from the corpus of contemporary american english (coca): in the first case, i.e. event reading, the nominalization lexicalizes the event denoted by the verb. this type of nominalization is also referred to as 'transpositional' in that the nominalization 'transposes' (recategorizes) the word from verb to noun without altering the sense of the verbal base. thus, disbursal in (1-a) can be paraphrased as "event of disbursing". in the case of result readings, the nominalization denotes "the outcome of verb-ing". thus, betrothal in (1-b) can be paraphrased as "the outcome of betrothing". finally, -al nominalizations may lexicalize the inanimate patient reading, that is, "the thing verb-ed, the thing affected by verb-ing". in (1-c), rental can be paraphrased as "the thing that someone rented". foot_0 the foregoing discussion suggests that the suffix -al can manipulate the frame of a verb of change of possession and target certain arguments of it. in particular, it can target the causation event argument (i.e. 0 ), the result state argument (i.e. 7 ), and the theme argument (i.e. 2 ). thus, the referent of a form derived by -al can be identified with some of arguments of the verbal base, but not all of them. observe, for instance, that the referent of -al derivatives is never the agent (i.e. 1 ), the recipient (i.e. ## modeling monosemy there are two approaches to multiplicity of meaning in derivation: monosemy and polysemy. in this section we examine the monosemy approach. under this approach, multiplicity of meaning is reduced by assigning a more vague meaning to an affix. thus, more concrete meanings of affixes derive from a general highly underspecified meaning. in order to apply the monosemy approach to -al, we have to reduce multiplicity of meaning by identifying meanings that are shared by all -al derivatives. as we saw in the previous section, -al derivatives denote (a) eventualities (e.g. event 'transpositional' readings), and (b) entities (e.g. inanimate theme readings). thus, the abstract core meaning of -al can be characterized as 'eventuality or entity having to do with x' (with 'x' denoting the base). monosemy approaches to the semantics of derivation are confronted with two problems to which we turn our attention. the first problem is that it is very hard to establish a unitary meaning for an affix. in particular, the aim of monosemy approaches is to reduce multiplicity of meaning by postulating a unitary abstract meaning. forms derived by -al, however, denote both eventualities and entities. thus, the disjunction 'eventuality or entity' that is needed in order to capture the multiplicity of meaning of -al derivatives reveals that the desirable underspecified meaning of affixes cannot always be reduced to a single unitary meaning. the second problem with the monosemy approach to the semantics of derivation is (massive) overgeneration. as we saw earlier, the abstract meaning for -al informs us that -al forms denote both eventualities and entities. this gives rise to the question: what kind of predictions follow from the abstract meaning 'eventuality or entity having to do with x'? this particular formulation of the abstract meaning of -al leads one to expect that -al derivatives could in principle denote all 'entities' and all 'eventualities'. our data, however, suggests that not all 'entities' and not all 'eventualities' can be denoted by -al derivatives. for instance, the referents of -al derivatives may be inanimate themes (e.g. houses in the case of rentals) but not recipients. the first xmg implementation we propose makes the modeling of the monosemy approach possible by using a scope-over constraint, expressing the fact that the reference of -al can be identified with any of the elements of the verbal base. we first need to describe the frame given in figure 1 , by means of a xmg reusable abstraction which we will name rent . this abstraction describes the class of verbs of change of possession: to define the scope-over relation mentioned earlier, we can use a new abstraction (a class we will name al_nominal). this class, as its name suggests, models the semantics of -al derivatives, which for the purposes of this study are based on verbs of change of possession. with import rent [ ], i.e. we make the structure defined in the class rent available in the current class, together with its variables (we can refer to all variables ?x0 ,..., ?x7 in the current class as they are exported by rent ). the @xmath1. concretely, the compiler will try to generate structures where the reference is identified with another label, starting with the whole frame (?x0), and then exploring all of its subparts, recursively. as we do not specify any other constraint here, the reference will be able to unify with every possible subpart. this means that readings such as initial state, which should be ruled out, are also generated when this first version of the metagrammar is executed. in this section we modeled the first approach to multiplicity meaning, i.e. monosemy, and showed that it leads to massive overgeneration. in the next section we focus on the second approach to multiplicity of meaning, i.e. polysemy. ## modeling polysemy under the polysemy approach, there is multiplicity of meaning in word formation patterns. given the architecture of frame semantics, this multiplicity of meaning can be expressed in an inheritance hierarchy of lexeme formation rules @xcite @xcite . thus, attested readings of words of a given morphological category result from indexation of particular elements (e.g. arguments) of the semantic representation of the verb, combined with inheritance mechanisms. an open question is how we can model the polysemy approach in xmg and constrain possible readings. we suggest that there are two ways to tackle this issue. first, via a fully specified (and explicit) rule, which will replace the scope over relation in the previous class al_nominal: under this approach, possible readings are considered as generalizations over already attested derivatives. thus, agent, recipient, and initial state readings are ruled out since they are not part of the possible readings in the fully-specified-rule; the rule models readings that are already attested in -al derivatives. the second way to model the polysemy approach in xmg is the introduction of an underspecified rule with constraints on types. in this case, the referent of an -al nominal can have three possible types: causation, result state, or entity. here, the first line is once again the scope over relation, but of course, in this case, only the structures where no type constraint is violated will eventually be generated. in the second line, we express the fact that the referent of an -al derivative can have any of the three types previously stated. in the case of entity, only the theme should be a possible referent. we, therefore, add information about animacy (here, inanimate), which makes the reference of -al derivatives incompatible with frames of type animate, such as the agent and the recipient. this is in accordance with findings in the literature on possible constraints on animacy (see lieber (2016) on -al and @xcite on the suffix -ment). when the referent of an -al derivative is a state, the type result_state is given to prevent unification with the initial state frame (of type initial_state ). this way, agent, recipient, and initial state readings are ruled out because frame unification only succeeds if types are compatible. the type constraints (for example incompatibility of event and entity) are also specified in the metagrammar. ## conclusion in a nutshell, our analysis allows one to model and test the various theoretical approaches to a long-standing issue in word formation. the xmg implementation revealed that the underspecified meaning of affixes cannot always be reduced to a single unitary meaning and that the monosemy approach leads to massive overgeneration. as we showed, the polysemy approach to multiplicity of meaning is more judicious compared to the monosemy approach. in order to deal with overgeneration, we proposed to introduce constraints on the potential referents of -al derivatives. these constraints have the form of type constraints and specify which arguments in the frame of the verbal base are compatible with the referential argument of the derivative. the introduction of type constraints rules out certain readings because frame unification only succeeds if types are compatible. in the present paper, we focused on -al derivatives which are based on verbs of change of possession. the next step is to apply the proposed analysis to other affixes and classes of bases as well. this will allow us to identify which constraints are specific to particular classes or affixes, and which constraints are shared across classes or affixes. of course, the main advantages of the metagrammatical framework will become more obvious as the linguistic resource grows: for example, inheritance will help sharing information across classes with similar behaviors.