Talk: Kote Razmadze (Tbilisi State University /Göttingen)

Title:

Temporal Logic of a Sequence of Finite Linear Processes

Abstract:

I provide a sound and complete axiomatization of a temporal logic of asequence of finitely many finite linear structures linked by surjective boundedmorphisms.

Finite linear structures, i.e., finite sets with a strict linear ordering, naturally arise as representations of a discrete, bounded time flow. Many domains of our everyday practice including time series, scene analysis, chain-of-responsibility design pattern in programming, etc. involve a finite linear structure to represent a sequence of consecutive steps. A familiar example of such a structure is a movie represented as a sequence of individual frames.

In such scenarios, it is often natural to group consecutive elements into conceptually meaningful units in such a way that these units inherit the temporal order of the original structure. Moreover, this process can be repeated finitely many times. For a typical example of what is meant here consider a set of movie frames, grouped into episodes, these further grouped into scenes, which finally form acts. The structure of episodes inherits the temporal order from the ordering of individual frames. The same is true for the structure of scenes, and that of acts.