Temporal Logics with Probabilistic Distributions

Talk by Alisa Kovtunova

Location: APB 3027
Start: 28. March 2019 at 1:00 pm
End: 28. March 2019 at 2:30 pm
Research group: Computational Logic
Research group: Automata Theory
Research group: Knowledge-Based Systems
Event series: KBS Seminar
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In many applications such as monitoring of dynamical systems, the data are actually time-dependent, e.g., describing the states of a dynamical system at different points in time. Moreover, events are more likely or less likely to happen in certain time points defined by the type of an event. There exist many well-studied distributions which can characterise the natures of events among us. For example, according to a Pareto distribution, a.k.a. a power-law distribution, the longer something has gone on, the longer we expect it to continue going on. Like new companies or start-ups, either (with the high probability) they fail during the first year of existence, or, if they manage to survive for decades, their chances of collapse are extremely small.

In order to capture dynamic time-dependent and probabilistic patterns of knowledge, using basic notions from probability theory and statistics, we have introduced temporal logics of expectation, where we can speak about statements not only occurring eventually in the future, but giving additional information on when they are likely to happen. The resulted combination of a temporal DL-Lite fragment (with a two-dimensional semantics, where one dimension is for time and the other for the DL domain) and an additional probabilistic constructor "distribution eventuality" is interpreted over multiple weighted worlds, viz., temporal DL interpretations.