Structures of opposition induced by relations The Boolean and the gradual cases

被引:29
作者
Ciucci, Davide [1 ]
Dubois, Didier [2 ]
Prade, Henri [2 ]
机构
[1] Univ Milano Bicocca, DISCo, Viale Sarca 336-14, I-20126 Milan, Italy
[2] Univ Toulouse 3, IRIT, 118 Route Narbonne, F-31062 Toulouse 9, France
关键词
Square of opposition; Composition of relations; Fuzzy relation; Multiple-valued logic; SQUARE; INFORMATION; POWER;
D O I
10.1007/s10472-015-9480-8
中图分类号
TP18 [人工智能理论];
学科分类号
081104 ; 0812 ; 0835 ; 1405 ;
摘要
The paper shows that a cube of opposition, a structure that generalizes the square of opposition invented in ancient logic, can be generated from the composition of a binary relation with a subset, by the effect of set complementation on the subset, on the relation, or on the result of the composition. Since the composition of relations is encountered in many areas, the structure of opposition exhibited by the cube of opposition has a universal flavor. In particular, it applies to information processing-oriented settings such as rough set theory, possibility theory, or formal concept analysis. We then discuss how this structure extends to a fuzzy relation and a fuzzy subset, and the graded cube of opposition thus obtained provides an organized view of the different existing compositions of fuzzy relations. The paper concludes by pointing out areas of research where the cube of opposition, or its graded version are of interest.
引用
收藏
页码:351 / 373
页数:23
相关论文
共 43 条
  • [1] Amgoud Leila, 2013, Symbolic and Quantitative Approaches to Reasoning with Uncertainty. 12th European Conference, ECSQARU 2013. Proceedings. LNCS 7958, P1, DOI 10.1007/978-3-642-39091-3_1
  • [2] [Anonymous], 4 ROUGH SET THEOR WO
  • [3] [Anonymous], 1846, T CAMBRIDGE PHILOS S
  • [4] [Anonymous], HDB 2 WORLD C SQUAR
  • [5] [Anonymous], TRADITIONAL SQUARE O
  • [6] [Anonymous], 2011, Probabilistic Metric Spaces
  • [7] [Anonymous], HDB 4 WORLD C SQUAR
  • [8] [Anonymous], 2012, NEW DIMENSIONS SQUAR
  • [9] [Anonymous], STUDIES EXERCISES 2
  • [10] [Anonymous], 1966, Structures Intellectuelles