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<p>The model of the structural part of Object Determination Logic (LDO) is translated and interpreted in the Formal Concept Analysis (FCA) model. In this article, we start from the premise that the modeling of a real problem has as its starting point a cognitive level that can be translated into the framework of a logic model and, subsequently, a mathematical model. We take these steps by considering the structural model of LDO, a lesser known and analyzed logic, and translating it into the FCA approach. Then, using the results of the analysis of the FCA model, we return to their interpretation within the LDO framework. Translation, i.e. the transition from the LDO model to the FCA model, is achieved by encoding in the FCA model, as faithfully as possible, each notion and constraint imposed by the LDO model. We illustrate this “methodology” by applying it to three situations corresponding to the cognitive elements of the LDO. The results obtained are interpreted from the point of view of cognitive elements of LDO. They enable us to establish the relationship between the LDO model and the FCA model, as well as the limits of each of the two models. On the basis of these limits, we propose an opening towards other types of mathematical models based on Soft Sets (SS) as parameterized sets.</p>

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On the Mathematical Modeling in Logic: An Analysis of the Structural Part of Object Determination Logic Through the Formal Concept Analysis

  • 期刊论文

  • 发表日期：

    2025年3月1日

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  • Anca Pascu,
  • Laurent Nana,
  • Jean Vareille,
  • François Monin

摘要

The model of the structural part of Object Determination Logic (LDO) is translated and interpreted in the Formal Concept Analysis (FCA) model. In this article, we start from the premise that the modeling of a real problem has as its starting point a cognitive level that can be translated into the framework of a logic model and, subsequently, a mathematical model. We take these steps by considering the structural model of LDO, a lesser known and analyzed logic, and translating it into the FCA approach. Then, using the results of the analysis of the FCA model, we return to their interpretation within the LDO framework. Translation, i.e. the transition from the LDO model to the FCA model, is achieved by encoding in the FCA model, as faithfully as possible, each notion and constraint imposed by the LDO model. We illustrate this “methodology” by applying it to three situations corresponding to the cognitive elements of the LDO. The results obtained are interpreted from the point of view of cognitive elements of LDO. They enable us to establish the relationship between the LDO model and the FCA model, as well as the limits of each of the two models. On the basis of these limits, we propose an opening towards other types of mathematical models based on Soft Sets (SS) as parameterized sets.