Strange goings on! Jones did it slowly, deliberately, in the bathroom, with a knife, at midnight. What he did was butter a piece of toast.
This he paraphrases into an informal logical form of `There is an action x such that Jones did x slowly and Jones did x deliberately and Jones did x in the bathroom...'. He proposes that actions are things and that, analogously to nominals which are associated with an index, the term which must be substituted for x is a variable associated with an event predicate. So in the case of dav11 we might represent the action and its modifying information as in dav12. Davidson argues that this representation allows us to maintain appropriate entailment relations among actions.
kamp_reyle:93 extend this idea from events to states, arguing that particular states can also be referred to in discourse. They distinguish between discourse referents (indices) for events and states explicitly by using es to refer to events and ss to refer to states (e, e', e'', ...and s, s', s'', ...). schilder:97 argues against this, preferring an analysis in which there is only one type of discourse referent, referring to situations. A situation can be either a state or an event. This allows Schilder to define a logic of temporal relations over situations in general, rather than having a separate treatment of states and events.
I will assume that there is a sort situation in the sort hierarchy which subsumes event and state, and which is defined for an index sit-ind.
Davis, in contrast, opts for having structure-sharing of content values instead of making use of a referential index. He adopts this approach not only for events but also for nominal objects. His motivation for this stems largely from linking issues (including some data on reflexives and the fact taht only one syntactic argument should realise a given semantic role), but also because he desires a uniform statement of the subcategorisations of verbs which allow either NP or VP/CP complements. In the original HPSG analysis of VP complements, there is full sharing of the content values of the VP complement and the soa-arg of the main verb's content, and Davis simply extends this mechanism to nouns for uniformity. The main criticism of this approach stems from the logical interpretation of the resulting feature structures: having full content values rather than indices serving as arguments to predicates results in a higher-order logic, so that rather than representing dav11 as dav12, we would have the interpretation dav26.
The logical complexity of the feature structure is therefore dramatically increased, making reasoning computationally less efficient. The entailment relations of the logical form in dav26 are also incorrect as there is nothing which forces the buttering event in the first conjunct to be the same as the one referred to in the second conjunct. I therefore prefer using indices for both nominals and events. All the feature structures previously given for Davis' relations will be modified to use indices rather than full content values as the values of the attributes (i.e. the values will be of type index rather than nom-obj). This change also allows for the fact that some nouns may refer to events and can therefore be associated with an event index. The problems which my choice creates for linking will need to be re-examined in future research, in the light of the logical complexity which Davis' choice leads to.
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