An important problem in artificial intelligence (AI) is to find calculation procedures to save the semantic gap between the analytic formulations of the neuronal models and the concepts of the natural language used to describe the cognitive processes. In this work we explore a way of saving this gap for the case of the attentional processes, consisting in (1) proposing in first place a conceptual model of the attention double bottom-up/top-down organization, (2) proposing afterwards a neurophysiological model of the cortical and sub-cortical involved structures, (3) establishing the correspondences between the entities of (1) and (2), (4) operationalizing the model by using biologically inspired calculation mechanisms (algorithmic lateral inhibition and accumulative computation) formulated at symbolic level, and, (5) assessing the validity of the proposal by accommodating the works of the research team on diverse aspects of attention associated to visual surveillance tasks. The results obtained support in a reasonable way the validity of the proposal and enable its application in surveillance tasks different from the ones considered in this work. In particular, this is the case when linking the geometric descriptions of a scene with the corresponding activity level.