Iterative Operations

ITERATIg-E OPERATIONS Sae Yamada Notre Dame Seishin University Ifuku-Ch5 2-16-9 700 Okayama, Japan ABSTRACT We present in this article, as a part of aspectual operation system, a gene- ration system of iterative expressions using a set of operators called iterative operators. In order to execute the itera- tive operations efficiently, we have classified previously propositions denoting a single occurrence of a single event into three groupes. The definition of a single event is given recursively. The classification has been carried out especially in consideration of the dura- tire / non-durative character of the denoted events and also in consideration of existence / non-existence of a cul- mination point (or a boundary) in the events. The operations concerned with iteration have either the effect of giving a boundary to an event ( in the case of a non-bounded event) or of extending an event through repetitions. The operators concerned are: N,F .. direct iterative operators; I,G .. boundary giving opera- tors; I .. extending operator. There are direct and indirect operations: the direct ones change a non-repetitious proposition into a repetitious one directly, whereas the indirect ones change it indirectly. The indirect iteration is indicated with . The scope of each operator is not uniquely definable, though the mutual relation of the operators can be given more or less explicitly. I INTRODUCTION The system of the iterative opera- tions, which makes a part of aspectual operation system, is based on the assump- tion that the general mechanism of repetition is language independent and can be reduced to a small number of operations, though language expressions of repetition are different from language to language. It must be noticed that even in one language there are usually several means to express repetitious events. We know that "il lui cognait la t~te contre lemur" and "il lui a cogn~ deux ou trois fois la t~te contre lemur", the examples given by W. Pollak, express the same event. We have also linguistic means for iterative expressions on all lin- guistic levels: morphological, syntactical, semantic, pragmatic etc. As the general form of repetition we use ~ = (~i~ in which ~ is the whole event, ~ia single occurrence of a single event and* an iteration indicator. For example: : (a series of) explosions took place 93: a single explosion took place : indefinit number of times ~i denotes actually a proposition describing a single event S i. ~ sign will be replaced later by a singIe or complex operator or operators, which operate(s) on ~i- We hope also to be able to give various expressions to the same event and for that purpose we are planning to have a set of interpretation rules. The language mainly concerned is Japanese, but in this article examples are given in French, in English or in German. 2 BASIC CONDITION OF THE ITERATION The iterative aspect is one of sentential aspect and denotes plural occurrence of an event or an action. The iterative aspect concerns therefore the property of countability. …

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