Professional profiles are unstructured documents where the knowledge and experience of the editor predominate, presenting inconsistencies and ambiguities in terms of the competencies they contain, making complicated the recognition of knowledge and skills necessary for the proposal of university study programs. Also, the identification of knowledge and skills in digital academic profiles present difficulties due to their inconsistencies. This work proposes analyzing the contradictions or ambivalences found in the academic and professional competencies published in digital media (for example, web pages or social networks) through a model of axioms based on dialetheic logic. Notably, the model considers five types of natural language phenomena: Vagueness or ambiguity, presupposition failure, counterfactual reasoning, fictional discourse, and contingent statements about the future. In addition, the model uses lexical and semantic similarity measures in its analysis process. The dialetheic model is validated using several performance measures to determine its capability to find ambiguity in a competence ontology described using description logic. The results show that dialetheic logic is required to accurately interpret digital academic and professional profiles using computational reasoning mechanisms. The model applies in a Spanish context for computer science jobs, with the possibility to apply in other languages or domains, such as English, French, etc. Our model is a contribution for competencies management, which is useful for the automatic curriculum design, competencies validation in learning processes, among other uses.