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The Category of L-Chu Correspondences and the Structure of L-Bonds

Kridlo O., Krajči S., Ojeda-Aciego M.

Fundamenta Informaticae

2012

Vol. 115, nr 4

297-325

An L-fuzzy generalization of the so-called Chu correspondences between formal contexts forms a category called L-ChuCors. In this work, we show that this category naturally embeds ChuCors and prove that it is *-autonomous. We also focus on the direct product of two L-fuzzy contexts, which is defined with the help of a binary operation, essentially a disjunction, on a lattice of truth-values L.

A Multimodal Logic Approach to Order of Magnitude Qualitative Reasoning with Comparability and Negligibility Relations

Burrieza A., Ojeda-Aciego M.

Fundamenta Informaticae

2005

Vol. 68, nr 1/2

21--46

Non-classical logics have proven to be an adequate framework to formalize knowledge representation. In this paper we focus on a multimodal approach to formalize order-of-magnitude qualitative reasoning, extending the recently introduced system MQ, by means of a certain notion of negligibility relation which satisfies a number of intuitively plausible properties, as well as a minimal axiom system allowing for interaction among the different qualitative relations. The main aim is to show the completeness of the formal system introduced. Moreover, we consider some definability results and discuss possible directions for further research.