Changes

|                                                          |

|                                                          |

|                      K          L                      |

|                      K          L                      |

|                      @           @                       |

|                      O           O                       |

|                      /|\        /|\                      |

|                      /|\        /|\                      |

|                    / | \      / | \                    |

|                    / | \      / | \                    |

|                      \  \  \  /                      |

|                      \  \  \  /                      |

|                        \ / \ / \ /                        |

|                        \ / \ / \ /                        |

|                        @   @   @                         |

|                        O   O   O                         |

|                        J  J  J                        |

|                        J  J  J                        |

|                                                          |

|                                                          |

|}

|}

Here, I have used arrowheads to indicate the relational domains at which each of the relations ''J'', ''K'', ''L'' happens to be functional.

Here, I have used arrowheads to indicate the relational domains at which each of the relations <math>J, K, L\!</math> happens to be functional.

Table&nbsp;20 gives the constraint matrix version of the same thing.

Table&nbsp;20 gives the constraint matrix version of the same thing.

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One way to read this Table is in terms of the informational redundancies that it schematizes.  In particular, it can be read to say that when one satisfies the constraint in the ''L'' row, along with all of the constraints in the ''J'' columns, then the constraint in the ''K'' row is automatically true.  That is one way of understanding the equation:  ''J''(''L''(''u'',&nbsp;''v'')) = ''K''(''Ju'',&nbsp;''Jv'').

One way to read this Table is in terms of the informational redundancies that it schematizes.  In particular, it can be read to say that when one satisfies the constraint in the <math>L\!</math> row, along with all the constraints in the <math>J\!</math> columns, then the constraint in the <math>K\!</math> row is automatically true.  That is one way of understanding the equation:  <math>J(L(u, v)) ~=~ K(Ju, Jv).</math>

===Commentary Note 11.14===

===Commentary Note 11.14===