How should we define inferential reasoning in high-level cognition? Can non-conscious representations guide or even determine high-level cognition? If so, what are the properties of such non-conscious representations? Two contemporary debates on high-level cognition center on these issues. The first concerns the possibility of cognitive penetration, or the degree and extent to which high-level cognition influences or determines low-level cognition. The second focuses on the epistemic status of conscious cognition, and on whether or not non-conscious cognition could play a similar, albeit not as fundamental, justificatory role as conscious cognition. This latter issue is at the heart of the question concerning the epistemic status of conscious awareness. This paper focuses on the epistemic standard required for inference, or inferential reasoning, to count as justificatory. The debates on the epistemic status of consciousness and cognitive penetration typically assume such a standard because high-level cognition is associated with rationality, inferentially structured thought, and the epistemic responsibility one has for the conclusions drawn through one's inferences. The paper proposes an account of inferential-attention that explains how cognitive penetration of non-phenomenally conscious cognition and perception is possible, and why there are unconscious processes that should be considered as essential components of high-level cognition. Sections "Defining Inference" and "Accuracy Constraints: The Agency-First Account of Inference" provide a theoretical framework for understanding the multiple criteria that an adequate account of inference and rational thought must satisfy. Sections "Attention: High- and Low-Level Inferential Cognition in Various Domains" and "Advantages Concerning Rule-Following and Rationality: Not Necessarily-Phenomenal Inferential Reasoning" articulate the inferential-attention account and explain how it meets the descriptive and normative criteria for epistemic responsibility and rationality. In particular, section "Attention: High- and Low-Level Inferential Cognition in Various Domains" defends an agential interpretation of inferential-attention, which offers a resolution of the tension between conservative or consciousness-based approaches to inference and liberal approaches that allow for types of unconscious or subdoxastic processes. An agency condition on inference explains how inference is a psychological process under the control of the agent, and at the same time, it satisfies the normative condition that an inference should be responsive to reasons or evidence by being cognitively available for personal level assessment and evaluation. The key is to identify this kind of epistemic agency with attention. Section "Advantages Concerning Rule-Following and Rationality: Not Necessarily-Phenomenal Inferential Reasoning" compares this inferential-attention account with an influential agential account of inference based on conscious intuition, and it argues that the former account is preferable. This section also demonstrates the significance of inferential-attention in higher cognition, even when it is non-phenomenally conscious.