Abstract
Formal Concept Analysis (FCA) theory relies on relational representation called formal context. Dealing with incomplete representations is a challenging issue in FCA. In this spirit, a Kripke structure has been proposed as semantics of three-valued Kleene’s logic for the exclusive definition of validity and possibility of attribute implications. Existing approaches consider possible intents as a set of attributes possibly satisfied by a given set of objects (a possible extent is dually considered). It appears that such a consideration is counter intuitive and quite misleading. Indeed, considering a possible intent as a whole granule of knowledge, in which each attribute is possibly satisfied by “all” objects, is a binding measure, in the sense that we cannot have possible intermediate granules of knowledge (i.e. intents or extents).
In this paper, we propose as a first stage, a new Kripke structure as semantics of modal logic. This structure is based on a completely different consideration, namely: “an object is a possible world”. As a second stage, a distance \( \delta \) that measures the implication strength \( o \rightarrow Y \) (dually \( p \rightarrow X \)) between an object o and a set of properties Y (dually between a property p and a set of objects X) is proposed. This distance which is recursively defined upon the accessibility relation, allows to bring an ordered set of possible worlds.
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Sadou, M., Djouadi, Y., Hadj-Ali, A. (2020). Modal Interpretation of Formal Concept Analysis for Incomplete Representations. In: Davis, J., Tabia, K. (eds) Scalable Uncertainty Management. SUM 2020. Lecture Notes in Computer Science(), vol 12322. Springer, Cham. https://doi.org/10.1007/978-3-030-58449-8_20
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DOI: https://doi.org/10.1007/978-3-030-58449-8_20
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