Multi-cloud computing has been proposed as a way to reduce vendor lock-in, to improve resiliency during outages and geo-presence, to boost performance and to lower costs. However, semantic differences between cloud providers, as well as their heterogeneous management interfaces, make changing from one provider to another very complex and costly. This is quite challenging for the implementation of multi-cloud systems. In this paper, we aim to take advantage of formal methods to define a precise semantics for multi-clouds. We propose fclouds, a formal-based framework for semantic interoperability in multi-clouds. This framework contains a catalogue of formal models that mathematically describe cloud APIs and reason over them. A precise alignment can be described between their concepts, which promotes semantic interoperability.