Language impairments in Alzheimer's disease (AD) primarily affect lexical and semantic levels, which significantly depend on the speaker's memory state. Qualitative shifts in semantic memory are due to neurodegenerative processes underlying dementia and give rise to anomia, or the speaker's inability to access and retrieve lexical units and their conceptual backgrounds. In this paper we aim at studying cognitive and semantic features of anomic deficit in AD and exploring the possibility to apply them in tests for early detection of dementia. For that purpose, we analyze the results from our experimental version of a classical test on semantic verbal fluency (SemVF) with nonpathological aged persons, persons with Mild Cognitive Impairment and persons with AD. The experimental version of the test introduces a division into four 15-minute intervals, in order to find out which processes of semantic access, either automatic or controlled, are impaired in different cognitive states of the elderly. Our results show a correlation between the cognitive state and the lexical-semantic ability of the speaker. Furthermore, they highlight, on the one hand, that the duration of the SemVF test should not be less than 60 seconds, with internal division into 4 15-second intervals, and, on the other hand, that some semantic categories-colours and fruit in particularare more prone to be affected by cognitive retrogenesis, which caracterizes AD dementia.