•  62
    Documentas del Concilio Vaticano II (review)
    Augustinianum 6 (3): 575-576. 1966.
  •  76
    On e^-definability in arithmetic
    with A. Fernandez-Marcarit and M. J. Perez-Jimenez
    In A. Rojszczak, J. Cachro & G. Kurczewski (eds.), Philosophical Dimensions of Logic and Science, Kluwer Academic Publishers. pp. 47--47. 2003.
  • On Overspill Principles and Axiom Schemes for Bounded Formulas
    with Mario Pérez-Jiménez and Alejandro Fernández-Margarit
    Mathematical Logic Quarterly 42 (1): 341-348. 2006.
    We study the theories I∇n, L∇n and overspill principles for ∇n formulas. We show that IEn ⇒ L∇n ⇒ I∇n, but we do not know if I∇n L∇n. We introduce a new scheme, the growth scheme Crγ, and we prove that L∇n ⇒ Cr∇n⇒ I∇n. Also, we analyse the utility of bounded collection axioms for the study of the above theories. Mathematics Subject Classification: 03F30, 03H15.
  • El Mesías y la realización de la justicia escatológica
    Salmanticensis 23 (1): 61-84. 1976.
  •  92
    FCA-based reasoning for privacy
    with Gonzalo A. Aranda-Corral and Juan Galán-Páez
    Logic Journal of the IGPL 32 (2): 224-242. 2024.
    Notwithstanding the potential danger to security and privacy, sharing and publishing data has become usual in Data Science. To preserve privacy, de-identification methodologies guided by risk estimation have been designed. Two issues associated with classical risk metrics are, on the one hand, the adequacy of the metric and, on the other hand, its static nature. In this paper, we present metrics for estimating risk based on the emerging semantics provided by Formal Concept Analysis. The metrics …Read more
  •  72
    On Overspill Principles and Axiom Schemes for Bounded Formulas
    with Alejandro Fernández-Margarit and Mario Pérez-Jiménez
    Mathematical Logic Quarterly 42 (1): 341-348. 1996.
    We study the theories I∇n, L∇n and overspill principles for ∇n formulas. We show that IEn ⇒ L∇n ⇒ I∇n, but we do not know if I∇n L∇n. We introduce a new scheme, the growth scheme Crγ, and we prove that L∇n ⇒ Cr∇n⇒ I∇n. Also, we analyse the utility of bounded collection axioms for the study of the above theories.
  •  49
    Algebraic combinatorics in bounded induction
    Annals of Pure and Applied Logic 172 (2): 102885. 2021.
  •  99
    Explainable Artificial Intelligence in Data Science
    with Juan Galán-Páez
    Minds and Machines 32 (3): 485-531. 2022.
    A widespread need to explain the behavior and outcomes of AI-based systems has emerged, due to their ubiquitous presence. Thus, providing renewed momentum to the relatively new research area of eXplainable AI (XAI). Nowadays, the importance of XAI lies in the fact that the increasing control transference to this kind of system for decision making -or, at least, its use for assisting executive stakeholders- already affects many sensitive realms (as in Politics, Social Sciences, or Law). The decis…Read more