As discussed in the introduction to this section, each of Jackendoff's function-argument structures is associated with a particular set of inferences. The functions are therefore used to capture similarities and differences in meaning conveyed by syntactically similar sentences. Although I will not endeavour to provide a complete overview of the function distinctions Jackendoff introduces in order to capture general inference patterns, the examples should give a flavour of the kind of analysis he undertakes.
The semantic distinction between the two different readings of the sentence in ji11a, from Jackendoff (1983:166) is captured by associating the preposition under with two different Path functions.
The mouse went under the table. The mouse arrived under the table. The mouse passed under the table. The mouse was under the table.
The first reading, that the mouse ran under the table and stayed there, is expressed by the Path function to, while the second reading, that the mouse passed under the table, is expressed by the Path function via. Only the first reading of the prepositional phrase is available in ji11b, while only the second reading is available in ji11c. Both of these uses of under must be distinguished from the use in ji11d, in which the prepositional phrase conveys a Place rather than a Path. The determination of which interpretation(s) of the preposition is (are) possible in each sentence depends on the meaning of the verb -- crucially captured in its lexical semantic representation, as shown in ji24. Under itself has three different interpretations, shown in ji25.
go 
arrive 
pass 
be 
under 
under 
under 
The Path argument of arrive is restricted to being a goal, i.e. a to Path and can therefore only combine with the ji25a interpretation of under. The Path argument of pass is restricted to being a route, i.e. a via Path, and can therefore only combine with the ji25b interpretation of under. Go is simply underspecified for what kind of Path argument it expects, thus allowing both interpretations of under to fill that argument position and accounting for the ambiguity of ji11a. The PP in ji11d is restricted to being a Place since the construction conveys that the PP is predicated of the subject; as it is not possible for the mouse to be the argument of a Path function but it is possible for it to be the argument of a Place function, due to ontological restrictions on what may serve as that argument, the PP must be interpreted as a Place, under the ji25c interpretation of under.
The discussion in Section 2.2.1 highlighted a difference
between verbs of motion and verbs of location and introduced the
representation Jackendoff proposes as underlying the distinction. The
functions in the representation do not simply constrain the kind of PP
arguments the different verb types can appear with, they also suggest
something about the relationship between the PP argument and the
subject of these sentences. From the
function-argument structure 
,
for example, we infer that the thing travels along
the path. Similarly, from 
we infer that the thing is in the location
place. Thus the functions each convey a particular meaning.
Additional support for the utility of the function-argument structures and their associated inference patterns comes from the fact that many of the functions which Jackendoff identifies can be extended from the spatial domain to other domains. Thus the go and be functions can be utilised within, for example, the domain of possession. It makes sense to utilise the same functions because the verbs represented with them can be used in the same syntactic frames as the spatial verbs and because the inferences associated with their use are simple extensions of the spatial inferences. Consider the sentences in ji17.
The doll belongs to Beth. Beth received the doll.
Sentence ji17a can be represented by ji18a and
ji17b by ji18b. The inference in the former case is
that the doll is possessed by Beth (a possessional extension of being
located at Beth), and in the latter that the doll transfers possession
to become Beth's (the possessional analogue of travelling along a path
which ends at Beth). These and other extensions of the basic spatial
functions suggest the utility of the functions identified by
Jackendoff and reflect regularities in use of language components
across domains (and, hopefully, across languages). More strongly, the
theory of the extensibility of spatial functions to other domains
results in a claim that many semantic fields have essentially the same
structure,
and that the spatial domain defines the terms in which many
kinds of discourse must be framed.