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According to RC theory, it entails processing the ternary relation linking three variables (deck, magnitude of gain, magnitude of loss).
The idea behind the ternary relation semantics is rather simple.
One interpretation of the ternary relation, due to Dunn, develops the idea behind Urquhart's semilattice semantics.
One problem with the semantics without the ternary relation is that it is difficult to use it to characterize as wide a range of logical systems as can done with the ternary relation.
Like the ternary relation semantics, this semantics requires some worlds to be inconsistent and some to be non-bivalent.
The ternary relation semantics can be adapted to be a semantics for a wide range of logics.
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However, ternary relations have not received as much attention, even though many real-world applications require the processing of ternary relations.
Then we propose two particular RAs: a binary RA, CYCb, whose universe is a set of (binary) relations on 2D orientations; and a ternary RA, CYCt, whose universe is a set of (ternary) relations on 2D orientations.
A first contribution of this work is the introduction of RAs whose universe is a set of ternary relations: these support rotation as an operation in addition to those present in Tarski's formalisation.
We show that all of these ternary relations are basic, and that the vast majority of them are R-relations.
The traditional mutual relationship is divided into two separate parts: the user can follow a user but does not always require the user to follow himself/herself (Golder and Yardi, [33]); indirect and closed ternary relations may exist (Boyd et. al, [34]).
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