Fuzzy Time Intervals for Simulating Actions

The paper presents time-related part of PSI1 theoretical framework. In comparison to other theories of time based on interval logics our approach presents the advancement by introducing fuzziness of time intervals as transition periods at beginnings and endings. It is argued that, though quite simple (discrete, linear, and anisotropic), our theoretical model is expressive enough to be used as a logical formalism for reasoning about stochastic, unpredictable, weakly defined action and process flows. A metric and a rich set of axiomatic relationships among time intervals are introduced for that. Further on, a means for modeling and reasoning about singular, repeated, regular events and actions having phases and vague durations is elaborated. Presented theory of time is used for modeling and reasoning about events, environmental influences, happenings, and actions while planning and scheduling in our simulations of dynamic engineering design processes.