Cloud-based elastic systems run on a cloud infrastructure and have the capability of dynamically adjusting the allocation of their resources in response to changes in the workload, in a way that balances the trade-off between the desired quality-of-service and the operational costs. The actual elastic behavior of these systems is determined by a combination of factors, including the input workload, the logic of the elastic controller determining the type of resource adjustment, and the underlying technological platform implementing the cloud infrastructure. All these factors have to be taken into account to express the desired elastic behavior of a system, as well as to verify whether the system manifests or not such a behavior. In this paper, we take a first step into these directions, by proposing a formalization, based on the CLTLt(D) temporal logic, of several concepts and properties related to the behavior of cloud-based elastic systems. We also report on our preliminary evaluation of the feasibility to check the (formalized) properties on execution traces using an automated verification tool.