Abstract
Formal Concept Analysis (FCA) extracts knowledge from an object-attribute relation. In the classical case, it focuses on positive information, i.e. attributes that are satisfied by objects. Several papers have recently been published extending FCA to manage negative information, i.e. attributes that are not satisfied by objects. However, the study of unknown information –being unknown, whether it is positive or negative value– is an issue to be explored. In this paper, we approach this problem by using a 4-valued logic. Specifically, given a context with partial information that corresponds to a 3-valued relation, we define a 4-valued Galois connection from where we extend the notions of concept and implication. Also, we present Amstrong’s axioms in this new framework, and we prove that this inference system is sound and complete.
Supported by Grants TIN2017-89023-P and PRE2018-085199 of the Science and Innovation Ministry of Spain and UMA2018-FEDERJA-001 of the Junta de Andalucia, and European Social Fund.
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Notes
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A mapping \(\varphi \) in \((L,\le )\) is antitone if \(x \le y\) implies \(\varphi (x) \ge \varphi (y)\), for all \(x,y\in L\).
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Pérez-Gámez, F., Cordero, P., Enciso, M., Mora, A. (2021). A New Kind of Implication to Reason with Unknown Information. In: Braud, A., Buzmakov, A., Hanika, T., Le Ber, F. (eds) Formal Concept Analysis. ICFCA 2021. Lecture Notes in Computer Science(), vol 12733. Springer, Cham. https://doi.org/10.1007/978-3-030-77867-5_5
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