Lexical decomposition of English spatial particles and their subsumption in motion constructions 1

In this paper, we firstly present a tentative formalization of a Lexical Template (LT) and a meta-language for spatial particle semantics within the framework of the Lexical Constructional Model (LCM). The semantic module consists of a set of Lexical Functions, which operate on a semantic primitive in order to produce a hyponym by elaborating topological, dynamic and functional information. The syntactic module expresses situations (positions or states) plus the argument structure. Secondly, we illustrate and discuss several LTs with the purpose of exploring spatial particle subsumption constraints with constructions such as caused motion and intransitive motion, as well as the types of verbal Aktionsart that might fuse with them. The COCA is used as a data source. We conclude that spatial particles contribute meaning to the extent that they partially determine the type of Aktionsart of the verb licensed by the motion construction.


I. INTRODUCTION
The first aim of this paper is to explore the lexical decomposition of spatial particles so as to introduce their lexical templates within the framework of the Lexical Constructional Model (henceforth LCM). Secondly, we discuss the semantic contribution of spatial particles to motion constructions, more precisely, to the Intransitive Motion Construction and the Caused Motion Construction. The current approach in Construction Grammar (Goldberg 1995: 164ff) avoids going into details about spatial particle meanings and holds that finite verbs fuse into constructions, so that whenever their semantic specifications do not match, the construction overrides the semantic value of the verb, thereby subsumed on the basis of the coercion principle.
Nothing is said about other lexical units participating in the construction, like spatial particles. Particle semantics is ignored, since the path is considered part of the constructional meaning: "the location encoded by the locative phrase is interpreted to be the endpoint of a path to that location" (Goldberg 1995: 159). Conversely, we claim that To provide evidence of our claim, that is, to show the meaning contributed by the particle and how that meaning matches the construction, we have carried out lexical decomposition in the form of lexical and constructional templates within the framework of the LCM.
The LCM (Butler 2009, Mairal and Ruiz de Mendoza 2008, 2009, Ruiz de Mendoza and Mairal 2007a, 2007b, 2008 proposes a semantic-syntactic system of representation of both lexical units and constructions. The use of a predicate, i.e., a lexical unit, in a particular construction is defined by a cognitive operation called subsumption (Peña 2009), which assumes both internal (semantic-syntactic) and external (pragmatic and discursive) constraints. The descriptive tools used for the formalization of subsumption processes are called Lexical Templates (henceforth LTs) and Constructional Templates (henceforth CTs), which share a common meta-language. LTs are semantic representations of the syntactically relevant content in the meaning of a lexical unit plus pragmatic and semantic information relevant to that meaning. CTs are similar formalizations of constructional meaning. Therefore, semantic decomposition of lexical predicates becomes necessary so as to determine the elements required in their semantic representation. In its attempt to provide a more adequate explanation for the syntactic-semantic interface, the LCM has a twofold goal: 1) Firstly, to identify the aspects of meaning which determine alternate usage of lexical units belonging to the same class, as well as to investigate why certain classes of lexical units participate in a given set of constructions while others do not.
2) Secondly, to provide a set of rules that regulates the fusion process (subsumption) considering semantic motivation at its basis. Contrary to most theories of lexical representation, the LCM claims that "a lexical rule should not only capture those idiosyncratic regularities that hold in the lexicon, but it should also explain the linguistic motivation that exists behind the generation of a given syntactic construction" (Mairal 2004: 11). We provide evidence that shows the kind of meaning contributed by the particle and how that meaning matches the construction. In accordance with the parameters set out above, enhanced formalism, as outlined by Mairal andFaber (2005, 2007) We have illustrated the structure of LTs and the meta-language employed in their semantic decomposition. The same kind of configuration and meta-language is used in the semantic description of constructions. CTs are present in different forms (e.g.

II. THE STRUCTURE OF LEXICAL AND CONSTRUCTIONAL TEMPLATES
argumental and idiomatic) at all levels of linguistic description (propositional, inferential, pragmatic and discursive). Thus, a CT is viewed as a high-level or abstract semantic representation of syntactically relevant meaning elements that are abstracted away from multiple lower-level representations, as in: (1) Paul walked into the room (2) Paul put the napkin in the drawer The CTs above encode motion constructions, so that, firstly, an entity (x) does an action (do). Moreover, in the intransitive motion construction, that entity (x) ends at location (z) by the effect of the action (do). The expression BECOME be-LOC' encodes the meaning 'change of location'. In the case of the caused motion construction, the action performed by (x) on another entity (y) causes that entity (y) to change its location.

III. LTS OF SPATIAL PARTICLES
In the following subsections, we introduce a characterization of the components in an LT of a spatial particle.

III.1. Argument structure
In Cognitive Grammar (Langacker 1987), spatial particles are considered lexical units of a relational nature, as are verbs: … a relationship is conceptually dependent on its participants. For example, we cannot conceptualize a spatial relation (like on, under, or near) without to some extent (if only schematically) invoking the entities that participate in it. As the term suggests, apprehending a relationship resides in conceiving entities in relation to one another. Thus it does not exist independently of those entities. (Langacker 2008: 200) English spatial particles are relational expressions, so that the speaker's conceptualization profiles interconnections among conceived entities. Interconnections are cognitive operations that assess the relative positions of entities within the scope of predication. As relational predicates, spatial particles profile a spatial relation on the basis of two other entities in the spatial domain. In the speaker's conceptualization, these two entitiestrajector and landmark -display an asymmetrical relationship in the same construal event as the relational concept as such.
Spatial particles express the construal of a situation where two entities are conceived as related to each other, and consequently can be regarded as the arguments of that predication. In that construal, the trajector is more salient once perceived and more dynamic than the landmark, which is secondary and more static. The former is the localized or foregrounded entity, and is construed as the movable element in the relationship. On the other hand, the landmark functions as a localizer, background or referential entity, construed as the static element or reference point in the relationship.
In terms of thematic frame, we say that the Logical Structure of spatial particles consists of two roles that are instantiated by the trajector and the landmark of the construal event. The term Logical Structure has been used in formal models of language to refer to verbal argument structure. The arguments of spatial predicates (x, y) designate the roles played by the trajector and the landmark. It is important to notice here that the terms trajector and landmark designate two participants in a construal event configuration, whereas arguments (x, y) are constructional functions of those participants.
Thus, in the context of the LCM it is realistic to represent the argument structure of spatial relational predicates as a combination of two arguments. In the LCM, therefore, at (x, y): The train at the station at (train, station) Spatial relations are, therefore, instantiated in language usage in the form of predications where the spatial predicate takes two arguments instantiated by the construed trajector and landmark, both being necessary for the conceptualization of the relationship expressed.

III.2. Semantic primitive
The NSM (Wierzbička 1996) provides a set of primitives that we adopt as a departure set in order to define the top of the conceptual hierarchy in the lexical domain of spatial can be designated by "speaker's location", ABOVE and BELOW by "higher level than" and "lower level than", and TOUCHING by "contact". 2 In the context of LCM formalization, the primitive MOVE can be identified with the expression [BECOME be-LOC' (y, z)], which expresses the fact that an entity y changes its location with respect to a place z. The intensifier VERY can be identified with the Lexical Function MAGN, which expresses intensification. The form "MORE" can be identified with the PLUS Lexical Function, which expresses a higher degree in relation to a reference point. In sum, each prime defines a subdomain of the lexical domain of spatial particles, which is represented in the syntactic module of an LT.

III.3. Lexical hierarchy
It is not assumed as an initial hypothesis that English has a particular word for each one of the primitives described above. We use the NSM list as our initial set of semantic primitives, i.e., as nuclear terms from which other terms can be defined by means of Lexical Functions.

III.4. Aktionsart distinctions
Aktionsart One of these Aktionsart configurations is assigned to a spatial particle LT, depending on which argument of the predication exerts control, according the construal configuration of the situation. Some spatial predicates express a first argument position, in the sense that the entity holds control of the relationship, like at or on, as in examples (3) and (4).
(3) The fly at the piece of melon In this line, Deane (1993Deane ( , 2005 proposed the multidimensional character of the semantic structure of spatial relations. According to that view, Navarro (2006)  We assume that every Lexical Function within an LT will correlate with one of these three experiential dimensions, as illustrated in Figure 2.

IV. SOME EXAMPLES OF SPATIAL PARTICLE LTS
In this section we introduce and discuss some LTs of spatial particles. Let us begin with the LT of the preposition at: At: [ -Argument structure including two arguments x and y. The former refers to the antecedent of the preposition and the latter to its complement (semantically construed as trajector and landmark, respectively).
-The semantic prime NEAR, expressing the fact that this preposition belongs to a lexical subdomain of relational predicates where the relationship designates proximity between the arguments.
-The expression (*[BECOME be-LOC (x)]) indicates that this preposition may participate in constructions where motion of argument x is expressed. The asterisk outside the square brackets and encircled between round brackets indicates that the predicate is compatible with constructions and other lexical items that express change of location, or movement, of the argument x, but this motion is not expressed by this particular predicate on its own.
-The term 'position' shows the situation type or interaction type expressed by this preposition. Particularly, it indicates that the first argument (x) is construed as a positioner in relation to the landmark (y), i.e., that the semantics of this particle implies certain control on the part of the trajector.

Lexical decomposition of English spatial particles and their subsumption in motion constructions
Language Value 3 (1), 114-137 http://www.e-revistes.uji.es/languagevalue 125 -Lexical Functions in the semantic module specify the semantics of the particle more precisely. Contiguity of trajector and Landmark is indicated by MAGN, which is an intensifier function of the topological aspect (T-) expressed by NEAR (proximity). The function D-INTENT 1 indicates dynamic intentionality of the first argument (x). The function F-PURP 1 indicates that the first argument is functionally oriented for some purpose. Finally, the function F-INSTR 2 indicates that the second argument is functionally conceived as an instrument or some manipulated entity.
(7) Laura (sat down) at the piano stretching her hands.
In (7)  The LT of the preposition in differs from the previous ones in several respects. In the meaning of this preposition the central role of a control parameter has been pointed out in previous research (Navarro 2000, Vandeloise 1994, 2005. In: The semantic prime INSIDE defines the lexical subdomain, expressing that the trajector (x) bears a spatial relationship with the inner side of the landmark. Motion is not expressed by the predicate itself, though it is compatible with dynamic contexts, as indicated by the asterisk. The situation type is a state where the trajector has no control, or position, but suffers instead, as an experiencer, the consequences of its location. The lexical function F-Control 2 expresses the idea that the second argument is viewed as a control factor over the trajector. Semantic shifts could result in pragmatically inferred senses such as protection, seclusion or others, which define the extensions of the semantic category.
(9) The present is in the box In (9) the conceived construal establishes a relationship between the trajector (present) and the inner side of the landmark (box). The relationship implies the limited or controlled mobility of the affected trajector (state), as effected by the landmark (F-Control 2 ).
The particle under presents a compound element in the slot for the nuclear term or primitive: near + below. Under: The LT of the particle "under" incorporates two primitive concepts. On the one hand, NEAR implies a proximity relationship whereas, on the other hand, BELOW indicates that the trajector is located at a lower level than the landmark. The asterisk preceding the expression [BECOME be-LOC (x)] expresses the compatibility of the particle with motion predicates. The situation type "state" signals the trajector's role as the experiencer. The  -constraint 2 ] shows that the relationship is functionally construed in such a way that the trajector is constrained by the landmark, either physically or otherwise.
(10) The man was caught under the log In (10) the entity "man" bears a relationship with the entity "log" so that the former is topologically near and below the latter. Functionally, "man" is seen as being in a state of constraint or restricted motion. It could be argued that the primitive "CONTACT" is also an attribute of the concept. However, not all contexts where this particle is used show contact between the participants. The Lexical Function of constraint accounts for a wider range of uses, including all those where CONTACT is also part of the conceptualization.
Next, we briefly discuss the contrast between onto and into versus on and in, respectively. Onto: [ As we can observe, the LT for these two particles have no asterisk accompanying the expression "[BECOME be-LOC (x)]". Therefore, the motion meaning is intrinsic to these particles, which must lead to the conclusion that no other motion predicates in the same construction are needed in order to express motion. In most other respects, the LTs coincide with on and in, respectively. The only difference between onto and on resides in a lexical function D-CONT that indicates the continuity of contact. As we see in (11b) and (12b), the sense of motion is contributed by the particle, and the role of the verb in (11a) and (12a) is reduced to express the manner of motion.
Following CG postulates, semantic properties specified for each parameter in these LTs are prototypical rather than requirements for each lexical unit or predicate. This fact implies that once we have determined the information in each of the components of the LT for a particular lexical unit or predicate, the result would represent the prototypical 128 semantics of that predicate, without taking into consideration partial sanction, semantic elaborations, shifts, or metaphorical extensions of that predicate category.

V. LEXICAL SUBSUMPTION
The LTs described above show the compatibility of particles with motion constructions.
In some cases, the motion meaning is required from other linguistic units (either lexical units or constructions), and in some other cases it is contributed by the particle itself In view of these remarks, we expect constructions to match the lexical specifications expressed by the LTs, either of verbs or particles, or both; otherwise the construction must override some of the predicate semantic specifications (Override Principle).
In addition to the general principles stated above, some cases of subsumption may require further constraint principles, as described by Mairal and Ruiz de Mendoza (2009: 188-192) and Peña (2009: 746): -Full matching: there must be full identification of variables, subevents, and operators between LTs and CTs.
-Event identification condition: correspondence is required between the various subevents (i.e., bundles of operators and variables) into which a lexical and constructional configuration can be segmented.
-Lexical blocking: one of the components of the LT can block the fusion with a certain construction given that this component is a suppletive form (e.g. kill, die).

Lexical decomposition of English spatial particles and their subsumption in motion constructions
Language Value 3 (1), 114-137 http://www.e-revistes.uji.es/languagevalue 129 -Predicate-argument conditioning: co-instantiation of a verbal predicate with one argument places restrictions on the kind of instantiating element that we can have for other constructional arguments.
-Internal variable conditioning: the internal predicate variables place constraints on the nature of both the predicate and constructional arguments.
Apart from these constraints, a process of accommodation or coercion may take place.
Coercion is only possible when a construction requires a particular interpretation that is not independently coded by particular LTs. The entire expression is judged grammatical to the extent that the occurring lexical items can be coerced by the construction into having a different but related interpretation to the one specified in their LTs. Therefore, the construction is able to coerce the locative term into a directional reading.
In this line, according to Goldberg, locative terms are coerced by the intransitive and the caused motion constructions into having a directional meaning related to their meaning, and "the location encoded by the locative phrase is interpreted to be the endpoint of a path to that location" (Goldberg 1995: 159). Conversely, our data show that it is not always the construction that coerces the spatial particle into having a directional meaning, but some particles contribute that meaning themselves. Interestingly enough, directional particles occur with much more frequency in motion constructions than nondirectional particles.
In the following section, we show patterns of occurrence of directional and non-directional particles in the constructions under scrutiny, i.e., intransitive motion and caused motion, as depicted above (see section 2).

CAUSED MOTION CONSTRUCTION
With the purpose of testing the degree of semantic relevance of the spatial particle in the subsumption process, we researched the co-occurrence of eight English prepositionsat, in, on, under, behind, over, onto, into - Tables I and II: 1. Stative verbs do not occur in motion constructions. However, certain spatial particles, like onto and into license causative stative verbs (e.g. scare) into the caused motion construction.
(13) …, to scare the kid onto the sidewalk.
(14) I think someone scared him into hiding.
2. All particles co-occur with active accomplishment verbs (e.g. come, get, put) in both constructions.
3. Only over and into co-occur with achievement verbs (e.g. shatter), in motion constructions in our sample.
(15) Glass shatters loudly all over the sink (16) … it isn't the candy that has shattered into rocky rubble, but my back molar

VII. DISCUSSION
In light of the results shown above, we may suggest some hypotheses about the semantic contribution of some particles in motion constructions.
The spatial particles into, over and onto contribute the semantic prime MOVE or [BECOME be-LOC (x)], that is, they express a trajector's change of location. This fact is reflected in the LTs of these particles and has also been proven by the examples in our  (22) and (23): In the oven, melt cheese on the croutes In view of these facts, we may suggest that spatial particles might be considered lexical entries that contribute some semantic content to the constructions they occur in, rather than just mere formal devices marking a locative argument.

VIII. FINAL REMARKS
The proposal presented here for a formalization of spatial particle LTs is rather tentative, given that no universal semantic meta-language has yet been established for topological, dynamic and functional spatial configurations. Further research points at the consolidation of a meta-language that expresses Lexical Functions of spatial particles in diverse languages.
The relevance of semantic descriptions of spatial particles may turn out to be more important than has been considered to date in cognitive functional models.
A further step is the investigation of subsumption constraints of spatial particle predicates in different constructions, since constructions like the Caused Motion Construction do not license all verbs. We could start by checking which spatial particles occur and which ones do not occur in the Caused Motion Construction, for instance, and then see whether a particular preposition licenses the use of certain verbs in the construction. For example, preliminary observations through corpus analyses suggest 134 that into and onto license some stative verbs in the Caused Motion Construction (e.g. she scared him into a depression).
Since spatial particles contribute meaning and are relational predicates (like verbs), we could account for some constructions as encompassing two predications, one as the main predication and the other as a secondary one. Each predication can be described in terms of argument structure. According to our view, spatial particles are predicates that relate two arguments, trajector and landmark, which may be shared by other relational predicates occurring in the same construction.
Finally, the metaphorical and figurative uses of spatial particles could also be studied as instantiations of external constraints in LCM.

Notes
1 Financial support for this research has been provided by the Fundació Bancaixa Castelló -Universitat Jaume I, grant P1 1A2010-14 and the Spanish Ministerio de Ciencia e Innovación, grant FFI2010-17610.
2 This is a terminological issue that we do not tackle here due to lack of space.
3 For a proper understanding of Table 1 and Table 2, the reader should take into account the following specifications: no = no instances have been found; ? = only one (or a few) dubious instances have been found; yes? = only one instance has been found; yes = some instances have been found; YES = the co-occurrence of the pair in the construction is very frequent.