Gradual Structures of Oppositions

There has been a renewal of interest in the use of squares of opposition and other related structures in the last decade, both for discussing issues in logical modeling and for their cognitive relevance. This paper outlines and motivates graded extensions of these structures (square, hexagon, cube, tetrahedron) of oppositions.

[1]  J. M. Dunn,et al.  Modern Uses of Multiple-Valued Logic , 1977 .

[2]  Béziau Jean-Yves.  New light on the Square of oppositions and its nameless corner , 2003 .

[3]  Enrique H. Ruspini,et al.  A New Approach to Clustering , 1969, Inf. Control..

[4]  Didier Dubois,et al.  Possibility Theory - An Approach to Computerized Processing of Uncertainty , 1988 .

[5]  Nuel D. Belnap,et al.  A Useful Four-Valued Logic , 1977 .

[6]  Vilém Novák,et al.  The analysis of the generalized square of opposition , 2013, EUSFLAT Conf..

[7]  Berthold Schweizer,et al.  Probabilistic Metric Spaces , 2011 .

[8]  Robert Blanche.  Sur l'opposition des concepts , 2008 .

[9]  Robert Blanché,et al.  Structures Intellectuelles : essai sur l'organisation systématique des concepts , 1981 .

[10]  Vilém Novák,et al.  Analysis of generalized square of opposition with intermediate quantifiers , 2014, Fuzzy Sets Syst..

[11]  Henri Prade,et al.  A Formal Concept View of Abstract Argumentation , 2013, ECSQARU.

[12]  Didier Dubois,et al.  From Blanché’s Hexagonal Organization of Concepts to Formal Concept Analysis and Possibility Theory , 2012, Logica Universalis.

[13]  Jean-Yves Béziau,et al.  The Power of the Hexagon , 2012, Logica Universalis.

[14]  Didier Dubois,et al.  Aggregation of Possibility Measures , 1990 .

[15]  L. Valverde,et al.  On Some Logical Connectives for Fuzzy Sets Theory , 1983 .

[16]  Didier Dubois,et al.  The Structure of Oppositions in Rough Set Theory and Formal Concept Analysis - Toward a New Bridge between the Two Settings , 2014, FoIKS.

[17]  Claudio Moraga,et al.  Multiple-Valued Logic and Artificial Intelligence Fundamentals of Fuzzy Control Revisited , 2003, Artificial Intelligence Review.

[18]  Henri Prade,et al.  Analogical Proportions and Square of Oppositions , 2014, IPMU.

[19]  Lotfi A. Zadeh,et al.  Similarity relations and fuzzy orderings , 1971, Inf. Sci..

[20]  Didier Dubois,et al.  An overview of the asymmetric bipolar representation of positive and negative information in possibility theory , 2009, Fuzzy Sets Syst..

[21]  Philippe Fortemps,et al.  A Graded Quadrivalent Logic for Ordinal Preference Modelling: Loyola–Like Approach , 2002, Fuzzy Optim. Decis. Mak..

[22]  Enric Trillas,et al.  Some remarks on approximate entailment , 1992, Int. J. Approx. Reason..

[23]  E. Trillas.  Sobre funciones de negación en la teoría de conjuntos difusos. , 1979 .

[24]  P. Kleingeld,et al.  The Stanford Encyclopedia of Philosophy , 2013 .

[25]  Enric Trillas,et al.  Characterizing non-monotonic fuzzy relations , 1997, Soft Comput..

[26]  L. Zadeh.  Fuzzy sets as a basis for a theory of possibility , 1999 .

[27]  Alexis Tsoukiàs,et al.  Paraconsistent semantics for Pavelka style fuzzy sentential logic , 2010, Fuzzy Sets Syst..