Simultaneous Events and the "Once-Only" Effect
Haythem Ismail
International Conference on Formal Ontology in Information Systems (FOIS 2006)
Baltimore, Maryland (USA), November 9-11, 2006
Abstract
Some events recur, and some happen only once. \cite{Galton84} refers to the latter as "once-only" events. In a first-order logic of events that makes a type-token distinction, the possibility of simultaneous occurrences of the same event renders the characterization of the intuitive once-onliness not very intuitive. In particular, the paradigmatic case of the $n^\mathrm{th}$ occurrence of a recurring event is shown to be not necessarily once-only. Counter-examples give rise to a classification of events based on the temporal relations among their occurrences. The problematic cases turn out to be those events that involve an indefinite individual; I call them indefinitely-specified events. Two options are considered. The first is to restrict our event ontology, as has been implicitly done in most logics of events, to events that are definitely-specified. The second is to admit all sorts of events into our ontology and distinguish those that are definitely-specified from those that are not by statements in the object language. I opt for a representation of events as functional terms in the logic and, consequently, terms denoting indefinitely-specified events seem to inevitably contain variables. Such non-ground terms turn out to be semantically problematic. To smoothly resolve these problems, I adopt Shapiro's logic of arbitrary and indefinite objects in which indefinite individuals are denoted by special terms \cite{Shapiro04}. Thus, indefinitely-specified events are naturally represented by functional terms with at least one argument denoting an indefinite individual.