Formal Concept Analysis from the Standpoint of Possibility Theory (ICFCA 2015)

Didier Dubois (1, 2) , Henri Prade (1, 2)

1 IRIT-ADRIA - Argumentation, Décision, Raisonnement, Incertitude et Apprentissage
2 CNRS - Centre National de la Recherche Scientifique

Formal concept analysis (FCA) and possibility theory (PoTh) have been developed independently. They address different concerns in information processing: while FCA exploits relations linking objects and properties, and has applications in data mining and clustering, PoTh deals with the modeling of (graded) epistemic uncertainty. However, making a formal parallel between FCA and PoTh is fruitful. The four set-functions at work in PoTh have meaningful counterparts in FCA; this leads to consider operators neglected in FCA, and thus new fixed point equations. One of these pairs of equations, paralleling the one defining formal concepts in FCA, defines independent sub-contexts of objects and properties that have nothing in common. The similarity of the structures underlying FCA and PoTh is still more striking, using a cube of opposition (a device extending the traditional square of opposition in logic). Beyond the parallel between FCA and PoTh, this invited contribution, which largely relies on several past publications by the authors, also addresses issues pertaining to the possible meanings, degree of satisfaction vs. degree of certainty, of graded object-property links, which calls for distinct manners of handling the degrees. Other lines of interest for further research are briefly mentioned.

Mots clés: Data mining and knowledge discovery; Information processing

Domaines: Intelligence artificielle [cs.AI]; Apprentissage [cs.LG]; Logique en informatique [cs.LO]; Informatique et langage [cs.CL]

Didier Dubois, Henri Prade. Formal Concept Analysis from the Standpoint of Possibility Theory (ICFCA 2015). 13th International Conference Formal Concept Analysis (ICFCA 2015), Jun 2015, Malaga, Spain. pp.21-38, ⟨10.1007/978-3-319-19545-2_2⟩. ⟨hal-01291629⟩