Degrees of truth, Ill-Known sets and contradiction

Didier Dubois (1, 2)

1 IRIT-ADRIA - Argumentation, Décision, Raisonnement, Incertitude et Apprentissage
2 QUB - Queen's University [Belfast]

In many works dealing with knowledge representation, there is a temptation to extend the truth-set underlying a given logic with values expressing ignorance and contradiction. This is the case with partial logic and Belnap bilattice logic with respect to classical logic. This is also true in three-valued logics of rough sets. It is found again in interval-valued, and type two extensions of fuzzy sets. This paper shows that ignorance and contradiction cannot be viewed as additional truth-values nor processed in a truth-functional manner, and that doing it leads to weak or debatable uncertainty handling approaches.

Domaines: Intelligence artificielle [cs.AI]

Didier Dubois. Degrees of truth, Ill-Known sets and contradiction. Bernadette Bouchon-Meunier; Luis Magdalena; Manuel Ojeda-Aciego; José-Luis Verdegay; Ronald R. Yager. Foundations of Reasoning under Uncertainty,, 249, Springer-Verlag, pp.65-83, 2010, Studies in Fuzziness and Soft Computing book series (STUDFUZZ), 978-3-642-10726-9. ⟨10.1007/978-3-642-10728-3_4⟩. ⟨hal-03416619⟩