Events and Memory in Functorial Time I: Localizing Temporal Logic to Condensed, Event-Dependent Memories


We develop an approach to temporal logic that replaces the traditional objective, agent- and event-independent notion of time with a constructive, event-dependent notion of time. We show how to make this event-dependent time entropic and hence well-defined. We use sheaf-theoretic techniques to render event-dependent time functorial and to construct memories as sequences of observed and constructed events with well-defined limits that maximize the consistency of categorizations assigned to objects appearing in memories. We then develop a condensed formalism that represents memories as pure constructs from single events. We formulate an empirical hypothesis that human episodic memory implements a particular constructive functor.

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