User:NemoNF/Homogeneous relation

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Homogeneous relation

A dyadic relation xRy is homogeneous when permuting referent x and relatum y in R, the resulting formula, i.e. yRx, is plausible but neither mandatory nor impossible.

Homogeneous polyadic predicate was defined by R. Carnap. When "from a sentence of n arguments, another sentence always arises as a result of any permutation of n arguments.The majority of the terms of relational theory refer to homogeneous binary predicates."1 Carnap, R., The logical structure of the world, The Regents of the University of California, 1967.

The homogeneity is not a new property of xRy apart from reflexive/irreflexive, symmetrical/anti-symmetrical and transitive/intransitive. It is a label[1] that applies when any of mentioned properties not always hold but only sometimes e.g. 'x functionally determines y' (x→y) is known to be reflexive, non-symmetrical and transitive; adding "x→y is homogeneous", means that y→x can hold for some couple of the set €U² where x≠y.

Let explain a case of homogeneity applying to the three main properties of a relation e.g. 'x loves y' (x♥y); (x♥y), as we know, is non-reflexive, non-symmetrical, non-transitive, then saying "x♥y is homogeneous" gives three times more information that the first example.

Finally, "xPy ('x father of y') is an heterogeneous relation" summarizes that xPy is irreflexive, anti-symmetrical and intransitive.