Both the Kasper (1993) and the vannoord_bouma:94 approaches generate a list on which adjuncts theoretically appear in order of their semantic obliqueness. Surface order of these adjuncts is then controlled by separate principles of constituent order. The motivation behind building these lists in terms of semantic obliqueness lies in the compositional approach to semantic interpretation in the two approaches.
The problem with these approaches is that they cannot easily account for the interaction between semantic scope of modification and surface order. Furthermore, it is not clear in either approach how or when the relative semantic obliqueness of adjuncts on these lists is determined. In the Kasper (1993) approach, a mechanism must exist which drives the insertion of elements into the adj-dtrs list, although it is not explicitly specified. This mechanism must also be responsible for evaluating the relative semantic obliqueness of inserted elements. It is not at all obvious how the surface order of the elements would be taken into account in this evaluation.
The vannoord_bouma:94 approach assumes that the parser hypothesises a structure for the subcat list of the head of a phrase which is evaluated against the constraints captured in the lexical rules. The hypothesised subcat list must therefore reflect consultation of linear precedence rules imposed upon the parser. These linear precedence rules must be able to generate a subcat list arranged in terms of semantic obliqueness from the surface order of the elements. Once the subcat list is hypothesised to be a list of elements in a certain order, the lexical rules adding adjuncts to the subcat list act to perform the appropriate semantic integration of the adjuncts into the overall representation of the verb semantics. Because the system treats these rules as constraints to be verified, no mechanisms controlling the relative order of adjuncts on the subcat list need be applied at the level of the rules. These mechanisms would be redundant.
This general approach is quite interesting, and effectively handles the word-order effects on the adjunct semantics if the linear precedence constraints are defined correctly. However, it is difficult to imagine how these constraints would be defined given that they would have to accommodate all variances in surface order among all adjunct types.
The approach presented here will restrict the domain of the constraints controlling semantic obliqueness to operator adjuncts. The constraints only need to take into account the relative semantic order of operator adjuncts, and will thus be easier to define. This restriction is possible since all other types of adjuncts provide information which actually modifies only the main sit-desc object associated with a verb. For example, in the sentences in d72, the ``John-jogged'' event is what is located in the park, regardless of the position of the restrictive PP relative to the operator adjuncts. It is not the ``twenty-minutes-duration (John-jogged)'' event which is located in the park, as would be suggested by (3.77b), or the ``twice-daily (twenty-minutes-duration (John-jogged))'' event which is located in the park, as suggested by (3.77c). All three of these sentences should have the interpretation ``twice-daily (twenty-minutes-duration (in-park (John-jogged)))''. Thus the semantic contribution of the restrictive adjunct must be incorporated before the operations specified by the operator adjuncts are processed.
John jogged in the park for twenty minutes twice a day. John jogged for twenty minutes in the park twice a day. John jogged for twenty minutes twice a day in the park.
Neither of the vannoord_bouma:94 and Kasper (1993) approaches handles these phenomena appropriately. Both approaches will give rise to errors in the semantic representation associated with a sentence containing interspersed operator and other adjuncts -- namely that the restrictive or thematic adjuncts will be seen as modifying complex operator soas rather than the main soa expressed by a sentence -- because they do not postpone evaluation of operator adjuncts until after the other types.
Because all adjuncts other than operator adjuncts provide information relevant to the main sit-desc associated with a verb, the semantic contribution made by these adjuncts can be incorporated into the structure representing the semantics of the situation being modified as soon as they are encountered (i.e. as soon as the adjuncts are inserted into the subcat list of the modified word by a lexical rule). On the other hand, operator adjuncts must always be processed after all other adjuncts, as evidenced by the example above.
To accommodate this difference between operator adjuncts and other adjuncts, I propose to make a distinction between the treatment of operator adjuncts and the treatment of other adjuncts. In the lexical rules controlling the treatment of all types of adjuncts other than operator adjuncts, the semantic contribution of these adjuncts is incorporated into the representation of the semantics of the situation immediately. For operator adjuncts, however, incorporation of their semantic contribution will be postponed until after all adjuncts have been inserted into the subcat list.
As operator adjuncts are added to the subcat list in a lexical rule, they are also added to an operator-adjuncts (op-adj) list associated with the synsem:cat of the lexical element whose subcat list is being manipulated. This will be used in the handling of semantic status and surface order interactions. The op-adj list will reflect the operator adjuncts in order of semantic obliqueness, while the subcat list reflects the surface order of all complements and adjuncts.
The approach involves keeping track of both surface order and relative semantic obliqueness of operator adjuncts. Following vannoord_bouma:94, the application of the lexical rules will be driven by a structure for the subcat list as proposed by the parser. However, this structure will reflect the natural surface order of the adjuncts rather than incorporating any evaluation of their semantic obliqueness. Thus linear precedence constraints on the parser will simply require that all adjuncts appear after the complements on the subcat list, with the adjuncts in surface order. The evaluation of semantic obliqueness will occur when an operator adjunct is added to the subcat list in a lexical rule. The evaluation function will be given the existing op-adj list and the new element, and then must determine the placement of the new element onto the list. This function will be able to take into consideration the relative surface order of the operator adjuncts, as any adjunct which it is attempting to insert into the op-adj list must appear later in the surface order than any elements already on the list.
After all operator adjuncts have been inserted into the op-adj
list, and the semantic contribution of all other adjuncts has been
integrated into the semantic representation for the situation as a
whole, the semantics of the operator adjuncts can be processed. The
op-adj list will contain all of the operator adjuncts, listed from
narrowest to widest scope. A function process_op_adjs
will essentially accomplish what Kasper's (1993) Adjunct
Semantics Principle does, but only for operator adjuncts: the
mod:loc:cont:nuc value of the adjunct of narrowest scope will
be made token identical to the sit-desc object representing the
situation. Then, if there are n > 1 elements on the op-adj
list, the mod:loc:cont:nuc value of op-adj 
is
token-identical with the synsem:loc:cont:nuc value of
op-adj 
for all i between 2 and n.
The result of this processing is a semantic value which then becomes
the semantics associated with the sentence as a whole.
In sum, the approach proposed here differentiates between operator and other adjunct types, integrating the semantics of other adjunct types immediately and postponing the semantic integration of operator adjuncts. This results in an appropriate representation of the semantics of sentences in which adjunct types are interspersed, and reflects the fact that only the semantic obliqueness of operator adjuncts relative to one another (but not to other adjunct types) plays a role in interpretation. The approach also allows the surface order of adjuncts to influence the evaluation of semantic obliqueness in a more straightforward manner by allowing the subcat list to reflect their surface order.