Early detection of Alzheimer's disease (AD) has become one of the principal focuses of research in medicine, particularly when the disease is incipient or even prodromic, because treatments are more effective in these stages. Lexical-semantic-conceptual deficit (LSCD) in the oral definitions of semantic categories for basic objects is an important early indicator in the evaluation of the cognitive state of patients. The objective of this research is to define an economic procedure for cognitive impairment (CI) diagnosis, which may be associated with early stages of AD, by analysing cognitive alterations affecting declarative semantic memory. Because of its low cost, it could be used for routine clinical evaluations or screenings, leading to more expensive and selective tests that confirm or rule out the disease accurately. It should necessarily be an explanatory procedure, which would allow us to study the evolution of the disease in relation to CI, the irregularities in different semantic categories, and other neurodegenerative diseases. On the basis of these requirements, we hypothesise that Bayesian networks (BNs) are the most appropriate tool for this purpose. We have developed a BN for CI diagnosis in mild and moderate AD patients by analysing the oral production of semantic features. The BN causal model represents LSCD in certain semantic categories, both of living things (dog, pine, and apple) and non-living things (chair, car, and trousers), as symptoms of CI. The model structure, the qualitative part of the model, uses domain knowledge obtained from psychology experts and epidemiological studies. Further, the model parameters, the quantitative part of the model, are learnt automatically from epidemiological studies and Peraita and Grasso's linguistic corpus of oral definitions. This corpus was prepared with an incidental sampling and included the analysis of the oral linguistic production of 81 participants (42 cognitively healthy elderly people and 39 mild and moderate AD patients) from Madrid region's hospitals. Experienced neurologists diagnosed these cases following the National Institute of Neurological and Communicative Disorders and Stroke/Alzheimer's Disease and Related Disorders Association (NINCDS-ADRDA)'s Alzheimer's criteria, performing, among other explorations and tests, a minimum neuropsychological exploration that included the Mini-Mental State Examination test. BN's classification performance is remarkable compared with other machine learning methods, achieving 91% accuracy and 94% precision in mild and moderate AD patients. Apart from this, the BN model facilitates the explanation of the reasoning process and the validation of the conclusions and allows the study of uncommon declarative semantic memory impairments. Our method is able to analyse LSCD in a wide set of semantic categories throughout the progression of CI, being a valuable first screening method in AD diagnosis in its early stages. Because of its low cost, it can be used for routine clinical evaluations or screenings to detect AD in its early stages. Besides, due to its knowledge-based structure, it can be easily extended to provide an explanation of the diagnosis and to the study of other neurodegenerative diseases. Further, this is a key advantage of BNs over other machine learning methods with similar performance: it is a recognisable and explanatory model that allows one to study irregularities in different semantic categories.