Autonomous intelligent agents must bridge computational challenges at disparate levels of abstraction, from the low-level spaces of sensory input and motor commands to the high-level domain of abstract reasoning and planning. A key question in designing such agents is how best to instantiate the representational space that will interface between these two levels -- ideally without requiring supervision in the form of expensive data annotations. These objectives can be efficiently achieved by representing the world in terms of objects (grounded in perception and action). In this work, we present a novel, brain-inspired, deep-learning architecture that learns from pixels to interpret, control, and reason about its environment, using object-centric representations. We show the utility of our approach through tasks in synthetic environments that require a combination of (high-level) logical reasoning and (low-level) continuous control. Results show that the agent can learn emergent conditional behavioural reasoning, such as $(A \to B) \land (\neg A \to C)$, as well as logical composition $(A \to B) \land (A \to C) \vdash A \to (B \land C)$ and XOR operations, and successfully controls its environment to satisfy objectives deduced from these logical rules. The agent can adapt online to unexpected changes in its environment and is robust to mild violations of its world model, thanks to dynamic internal desired goal generation. While the present results are limited to synthetic settings (2D and 3D activated versions of dSprites), which fall short of real-world levels of complexity, the proposed architecture shows how to manipulate grounded object representations, as a key inductive bias for unsupervised learning, to enable behavioral reasoning.