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Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 6 (view source)
Revision as of 02:44, 7 January 2013
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This Section introduces a topic of fundamental importance to the whole theory of sign relations, namely, the question of whether triadic relations are ''determined by'', ''reducible to'', or ''reconstructible from'' their dyadic projections.
This Section introduces a topic of fundamental importance to the whole theory of sign relations, namely, the question of whether triadic relations are ''determined by'', ''reducible to'', or ''reconstructible from'' their dyadic projections.
Suppose <math>L \subseteq X \times Y \times Z\!</math> is an arbitrary triadic relation and consider the information about <math>L\!</math> that is provided by collecting its dyadic projections. To formalize this information define the ''projective triple'' of <math>L\!</math> as follows:
<pre>
<pre>
Proj (R) = Pr2(R) = <Pr12(R), Pr13(R), Pr23(R)>.
Proj (R) = Pr2(R) = <Pr12(R), Pr13(R), Pr23(R)>.