A Formal Representation Of Propositions And Temporal Adverbials

The topic of the paper is the introduction of a formalism that permits a homogeneous representation of definite temporal adverbials, temporal quantifications (as frequency and duration), temporal conJ~ctions and tenses, and of their combinations with propositions. This unified representation renders it possible to show how these components refer to each other and interact in creati~ temporal meanings. The formal representation is 0ased on the notions "phase-set" and "phase-operator", and it involves an interval logic. Furthermore logical coz~uections are used, but the (always troublesome) logical quantifications may be avoided. The expressions are rather near to lingaistic structures, which facilitates the link to text analysis. Some emprical confirmations are outlined. q. THE GENERAL FRAME This paper presents some results that have been obtained in the field of time and tense-phenomena (K~Luze 1987). In connection with this some links to text analysis, knowledge representation and q~erence mechanisms have been taken into accoumt. The formalism presented here differs from what is under label of temporal logic on the market (e. g. Prior (1967), Aqviet/Guenthner (1978). Our main intention is to establish a calculus that is rather near to linguistic structures on one side (for text analysis) and to inference mechanisms on the other side. The whole formalism has integrating features, i. e. the following components are represented by the same formal means in a way, that it becomes easy and effective to refer the different components to each other: The propositions and their validity with respect to time; Definite temporal adverbials (nex~ wee k , ever~ Tuesda2); Definite temporal qu~uti£ications as frequency (three times) and duration (three hours), comparislon of frequencies, durations etc.; Temporal conj~ctlons; Tenses and their different meanings. The unified representation renders it possible to observe how the components interact in creating temporal meanings and relations. Some details have to be left out here, e. g. the notion "determined time" and the axiomatic basis of the calculus.