Resilience is commonly understood as the capacity for a system to maintain a desirable state while undergoing adversity or to return to a desirable state as quickly as possible after being impacted. In this paper, we focus on resilience for complex sociotechnical systems (STS), specifically those where safety is an important aspect. Two main desiderata for safety-critical STS to be resilient are adaptive capacity and adaptation. Formal studies integrating human cognition and social aspects are needed to quantify the capacity to adapt and the effects of adaptation. We propose a conceptual framework to elaborate on the concept of resilience of safety-critical STS, based on adaptive capacity and adaptation and how this can be formalized. A set of mechanisms is identified that is necessary for STS to have the capacity to adapt. Mechanisms belonging to adaptive capacity include situation awareness, sensemaking, monitoring, decision-making, coordination, and learning. It is posited that the two mechanisms required to perform adaptation are anticipation and responding. This framework attempts to coherently integrate the key components of the multifaceted concept of STS Equationsadaptive resilience. This can then be used to pursue the formal representation of Equationsadaptive resilience, its modeling, and its operationalization in real-world safety-critical STS.