On the modal understanding of triadic contexts

A triadic context consists of sets of formal objects, formal attributes, and formal conditions together with the formalization of the ternary relation saying when an object has an attribute under a certain condition. The modal understanding of necessity and possiblity occurs naturally in triadic contexts, especially when the dyadic relationships between formal objects and attributes are considered: a formal object g has “necessarily” a formal attribute m if g has m under all formal conditions of the context; g has “possibly” m if g has m under some formal condition. Such necessity and possibility relations give rise to dyadic contexts allowing a modal analysis of triadic data contexts. How this analysis can be approached is shown by examples. Theoretically, we point out how a “modal Attribute Logic” may be developed.

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