The enactive inference task is the task for an autonomous enactive artificial agent to infer data structures useful to select future adapted behavior. An enactive artificial agent is an agent that experiences its environment through motor sensory loops rather than passively receiving data that represent the environment’s state. Motor Sensory loops are loops of actuator commands and non-representational sensory signal. The measure of behavioral adaptation does not need to be computed by the agent; it can be judged by an observer upon criteria such as self-motivation, playfulness, curiosity, or learning. We review the literature on Dynamic Bayesian Networks and on Partially Observable Markov Decision Processes to propose a new formalism to study the enactive inference task called Spatial Enactive Markov Decision Process (SEMDP). An SEMDP implements the presupposition that the interactional domain has a three-dimensional spatial structure. This is illustrated in a proof-of-concept experiment in which a robot infers the shape of its environment. The enactive inference task formalized as an SEMDP is tractable; it can be performed by a finite-memory algorithm, and does not involve reaching predefined goals associated with a predefined set of states.