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<pre>
−Table 5. Ef Expanded Over Differential Features {dx, dy}
−o------o------------o------------o------------o------------o------------o
−| | | | | | |
−| | f | T_11 f | T_10 f | T_01 f | T_00 f |
−| | | | | | |
−| | | Ef| dx dy | Ef| dx(dy) | Ef| (dx)dy | Ef|(dx)(dy)|
−| | | | | | |
−o------o------------o------------o------------o------------o------------o
−| | | | | | |
−| f_0 | () | () | () | () | () |
−| | | | | | |
−o------o------------o------------o------------o------------o------------o
−| | | | | | |
−| f_1 | (x)(y) | x y | x (y) | (x) y | (x)(y) |
−| | | | | | |
−| f_2 | (x) y | x (y) | x y | (x)(y) | (x) y |
−| | | | | | |
−| f_4 | x (y) | (x) y | (x)(y) | x y | x (y) |
−| | | | | | |
−| f_8 | x y | (x)(y) | (x) y | x (y) | x y |
−| | | | | | |
−o------o------------o------------o------------o------------o------------o
−| | | | | | |
−| f_3 | (x) | x | x | (x) | (x) |
−| | | | | | |
−| f_12 | x | (x) | (x) | x | x |
−| | | | | | |
−o------o------------o------------o------------o------------o------------o
−| | | | | | |
−| f_6 | (x, y) | (x, y) | ((x, y)) | ((x, y)) | (x, y) |
−| | | | | | |
−| f_9 | ((x, y)) | ((x, y)) | (x, y) | (x, y) | ((x, y)) |
−| | | | | | |
−o------o------------o------------o------------o------------o------------o
−| | | | | | |
−| f_5 | (y) | y | (y) | y | (y) |
−| | | | | | |
−| f_10 | y | (y) | y | (y) | y |
−| | | | | | |
−o------o------------o------------o------------o------------o------------o
−| | | | | | |
−| f_7 | (x y) | ((x)(y)) | ((x) y) | (x (y)) | (x y) |
−| | | | | | |
−| f_11 | (x (y)) | ((x) y) | ((x)(y)) | (x y) | (x (y)) |
−| | | | | | |
−| f_13 | ((x) y) | (x (y)) | (x y) | ((x)(y)) | ((x) y) |
−| | | | | | |
−| f_14 | ((x)(y)) | (x y) | (x (y)) | ((x) y) | ((x)(y)) |
−| | | | | | |
−o------o------------o------------o------------o------------o------------o
−| | | | | | |
−| f_15 | (()) | (()) | (()) | (()) | (()) |
−| | | | | | |
−o------o------------o------------o------------o------------o------------o
−| | | | | |
−| Fixed Point Total | 4 | 4 | 4 | 16 |
−| | | | | |
−o-------------------o------------o------------o------------o------------o
−</pre>
I will first rationalize the novel grouping of propositional forms in the last set of Tables, as that will extend a gentle invitation to the mathematical subject of group theory, and demonstrate its relevance to differential logic in a strikingly apt and useful way. The data for that account is contained in Table 5.
I will first rationalize the novel grouping of propositional forms in the last set of Tables, as that will extend a gentle invitation to the mathematical subject of group theory, and demonstrate its relevance to differential logic in a strikingly apt and useful way. The data for that account is contained in Table 5.
−The shift operator ''E'' can be understood as enacting a substitution operation on the proposition that is given as its argument. In our immediate example, we have the following data and definition:
The shift operator ''E'' can be understood as enacting a substitution operation on the proposition that is given as its argument. In our immediate example, we have the following data and definition:
