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SIGH. Note 11
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Family Interaction Dataset as a Two-Level Formal Language (cont.)
In the ideal situation, a language ought to have a grammar.
It has often been observed that a grammar is tantamount to
a rational theory of the empirical language, subsuming the
infinite variety of a linguistic corpus, passed or present
or prospective, under the capitation of a finite mentality.
In the empirical situation, however, always in the beginning far from ideal,
the grammar of a language is a datum that awaits discovery at a future date.
On the other hand, the experience that a finite mentality has actually
experienced at any given time is of necessity a finite experience, and
so it is possible to organize the experienced language in a finite way,
even though it is likely to be far away from the ideal grammar, namely,
in the form of "finite state transition graphs" (FST graphs). In this
way, a k-level formal language can be recorded as it enters experience
in the form of k FST graphs, one graph for each level of the language.
In particular, it is especially feasible under realtime conditions to
keep track of the language actually experienced by means of FST trees.
A k-level formal language can be recorded as it comes into experience
by means of a k-tuple of FST trees, using one tree to rule each level.
Among the possible variety of data models, one has the option of using either
"free order" or "fixed order" FST trees. In the case of a 2-FL we get a pair
of FST trees that may be referred to as the "lexical" and the "literal" trees.
At this point, though, it is probably best to return to our concrete datasets.
I will next illustrate how the family interaction data looks when arranged as
a pair of free order FST's. For the sake of comparison, and also because the
first dataset is somewhat amorphous from this point of view, I will list here
a second dataset, a father-child dyad from the same family, with what I think
to be the same child, but I no longer have the corresponding demographic data.
Family Interaction Analysis. Abbreviated Dataset 2
------------------------------------------------------------------------
TRIAL FAMILY SESSION FOCUS OBSERVER FAMILY MEMBERS MO/DY/YR HR:MN
1 MXYZ 5 1 22 12000000 12/03/86 13:34
------------------------------------------------------------------------
| 9 99 9 0
|
| 1 12 2 2
| 2 12 3 4
| 1 62 2 8
| 2 12 3 11
| 1 62 2 13
| 1 12 3 15
| 2 12 3 21
| 2 32 3 24
| 1 12 3 29
| 1 01 3 31
| 2 73 3 38
| 2 12 3 41
| 1 12 3 42
| 2 12 3 44
| 1 12 2 50
| 2 12 3 52
| 2 32 3 62
| 1 53 3 65
| 1 13 4 70
| 1 62 3 73
| 2 12 3 76
| 9 99 9 83
|
| 1 62 2 85
| 1 12 3 88
| 2 12 3 90
| 1 12 3 91
| 2 12 3 93
| 1 12 2 97
| 2 12 2 99
| 1 12 2 102
| 9 99 9 109
|
| 1 12 2 112
| 2 62 2 115
| 1 12 2 117
| 2 12 3 120
| 2 13 4 123
| 1 12 2 126
| 1 62 2 128
| 1 12 2 131
| 2 12 3 133
| 1 12 3 135
| 2 12 3 139
| 1 32 4 147
| 2 01 3 152
| 1 12 3 156
| 2 12 3 158
| 1 12 3 159
| 2 12 3 162
| 1 32 3 164
| 2 12 3 167
| 1 12 4 173
| 2 12 3 179
| 1 12 3 182
| 2 32 3 187
| 1 01 3 189
| 2 32 3 193
| 1 01 2 195
| 1 12 2 199
| 2 32 3 202
| 1 01 3 205
| 2 12 3 209
| 1 62 2 210
| 9 99 9 218
|
| 1 62 2 222
| 1 12 2 225
| 1 12 1 229
| 2 32 3 235
| 1 62 2 239
| 2 13 4 244
| 2 32 3 253
| 1 12 3 254
| 1 01 3 258
| 2 11 3 259
| 1 62 2 263
| 2 12 3 265
| 1 12 2 267
| 2 32 3 270
| 1 01 3 274
| 1 12 3 278
| 2 32 3 282
| 1 01 3 286
| 2 12 3 287
| 1 12 2 289
| 2 11 3 292
| 1 12 3 295
| 2 12 3 299
| 1 12 3 303
| 2 12 2 305
| 1 73 4 313
| 1 12 4 320
| 2 12 3 322
| 1 12 4 323
| 2 12 3 326
| 1 12 4 328
| 2 62 3 332
| 1 12 3 334
| 2 12 3 338
| 1 32 3 339
| 2 12 3 346
| 2 01 3 352
| 1 62 2 355
| 9 99 9 360
|
| 1 42 3 364
| 2 12 2 369
| 2 01 3 371
| 1 12 3 375
| 1 32 3 379
| 2 32 3 382
| 1 12 3 385
| 2 12 3 388
| 1 12 3 390
| 2 12 3 392
| 1 22 3 396
| 2 32 3 405
| 1 01 3 409
| 2 12 3 412
| 2 32 3 417
| 1 01 3 419
| 2 12 3 424
| 2 32 3 427
| 1 01 3 429
| 9 99 9 436
|
| 1 62 2 437
| 2 12 2 443
| 1 12 2 445
| 2 32 3 448
| 1 01 3 449
| 2 92 3 455
| 1 62 2 462
| 1 12 2 465
| 2 12 3 467
| 1 12 3 469
| 2 12 3 471
| 1 62 3 472
| 2 12 3 474
| 1 12 2 477
| 9 99 9 485
|
| 1 62 2 489
| 2 13 4 496
| 1 12 3 499
| 2 12 3 502
| 1 12 2 509
| 2 12 3 513
| 1 42 3 514
| 2 01 3 518
| 1 12 3 523
| 1 62 2 527
| 1 12 2 531
| 2 12 3 539
| 1 62 2 541
| 1 12 2 544
| 2 12 3 547
| 1 12 2 550
| 2 12 3 554
| 1 12 3 557
| 2 12 2 564
| 1 12 3 569
| 2 12 3 573
| 1 12 3 574
| 2 12 3 575
| 1 12 3 577
| 2 12 3 579
| 1 62 3 594
| 9 99 9 597
Here is the literal level of Dataset 2 presented as a free order FST
in outline form. The numbers at the right give the frequencies with
which the corresponding node of the tree is traversed in the session.
Reading this display we see that there are seven distinct strands in
the second level of the associated 2-FL:
4 strands begin with 1_62_2, Child vocalizes with positive affect.
2 strands begin with 1_12_2, Child talks with positive affect.
1 strand begins with 1_42_3, Child ambiguously commands with neutral affect.
| dataset_2 7
| 1_62_2 4
| 1_12_3 1
| 2_12_3 1
| 1_12_3 1
| 2_12_3 1
| 1_12_2 1
| 2_12_2 1
| 1_12_2 1
| * 1
| 1_12_2 1
| 1_12_1 1
| 2_32_3 1
| 1_62_2 1
| 2_13_4 1
| 2_32_3 1
| 1_12_3 1
| 1_01_3 1
| 2_11_3 1
| 1_62_2 1
| 2_12_3 1
| 1_12_2 1
| 2_32_3 1
| 1_01_3 1
| 1_12_3 1
| 2_32_3 1
| 1_01_3 1
| 2_12_3 1
| 1_12_2 1
| 2_11_3 1
| 1_12_3 1
| 2_12_3 1
| 1_12_3 1
| 2_12_2 1
| 1_73_4 1
| 1_12_4 1
| 2_12_3 1
| 1_12_4 1
| 2_12_3 1
| 1_12_4 1
| 2_62_3 1
| 1_12_3 1
| 2_12_3 1
| 1_32_3 1
| 2_12_3 1
| 2_01_3 1
| 1_62_2 1
| * 1
| 2_12_2 1
| 1_12_2 1
| 2_32_3 1
| 1_01_3 1
| 2_92_3 1
| 1_62_2 1
| 1_12_2 1
| 2_12_3 1
| 1_12_3 1
| 2_12_3 1
| 1_62_3 1
| 2_12_3 1
| 1_12_2 1
| * 1
| 2_13_4 1
| 1_12_3 1
| 2_12_3 1
| 1_12_2 1
| 2_12_3 1
| 1_42_3 1
| 2_01_3 1
| 1_12_3 1
| 1_62_2 1
| 1_12_2 1
| 2_12_3 1
| 1_62_2 1
| 1_12_2 1
| 2_12_3 1
| 1_12_2 1
| 2_12_3 1
| 1_12_3 1
| 2_12_2 1
| 1_12_3 1
| 2_12_3 1
| 1_12_3 1
| 2_12_3 1
| 1_12_3 1
| 2_12_3 1
| 1_62_3 1
| * 1
| 1_42_3 1
| 2_12_2 1
| 2_01_3 1
| 1_12_3 1
| 1_32_3 1
| 2_32_3 1
| 1_12_3 1
| 2_12_3 1
| 1_12_3 1
| 2_12_3 1
| 1_22_3 1
| 2_32_3 1
| 1_01_3 1
| 2_12_3 1
| 2_32_3 1
| 1_01_3 1
| 2_12_3 1
| 2_32_3 1
| 1_01_3 1
| * 1
| 1_12_2 2
| 2_12_3 1
| 1_62_2 1
| 2_12_3 1
| 1_62_2 1
| 1_12_3 1
| 2_12_3 1
| 2_32_3 1
| 1_12_3 1
| 1_01_3 1
| 2_73_3 1
| 2_12_3 1
| 1_12_3 1
| 2_12_3 1
| 1_12_2 1
| 2_12_3 1
| 2_32_3 1
| 1_53_3 1
| 1_13_4 1
| 1_62_3 1
| 2_12_3 1
| * 1
| 2_62_2 1
| 1_12_2 1
| 2_12_3 1
| 2_13_4 1
| 1_12_2 1
| 1_62_2 1
| 1_12_2 1
| 2_12_3 1
| 1_12_3 1
| 2_12_3 1
| 1_32_4 1
| 2_01_3 1
| 1_12_3 1
| 2_12_3 1
| 1_12_3 1
| 2_12_3 1
| 1_32_3 1
| 2_12_3 1
| 1_12_4 1
| 2_12_3 1
| 1_12_3 1
| 2_32_3 1
| 1_01_3 1
| 2_32_3 1
| 1_01_2 1
| 1_12_2 1
| 2_32_3 1
| 1_01_3 1
| 2_12_3 1
| 1_62_2 1
| * 1
Jon Awbrey
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