Formalize goal-directedness for STP-based entities

Develop a formal definition of goal-directedness applicable to entities represented as spatiotemporal patterns within finite, time-discrete multivariate Markov chains, enabling rigorous analysis of how goal-directedness interacts with the notion of action and the exclusion of random events as agent actions.

Background

In introducing actions for entities defined as spatiotemporal patterns, the authors discuss the treatment of randomness and note that distinguishing genuine actions from random events may depend on the entity-set and goal-directedness. They explicitly state that no formal definition of goal-directedness is currently available.

A formal notion of goal-directedness is needed to assess when actions should be considered purposeful and to resolve whether random events should be excluded from being interpreted as actions of agents.