ONT Re: Model Theory -- Data In Logic
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Here is a sample data set, represented in propositional logic.
This data comes from a "real live" and major funded research study
on parent-child interactions. I was allowed to use a small portion
of this data to test out the qualitative data analysis software that
I wrote as one part of my Master's work in Quantitative Psychology.
I have been meaning to trot this out ever since Howard raised the
issue of "logic and data entry" a while back, but I think that it
now acquires a measure of newfound relevance in connection with
the issues of "empirical content in logic" that John and I have
been going round about lately under this heading. To save me
the effort of writing a new seque for this piece, here is how
I introduced this way of looking at "sequential interactions"
to the Conceptual Graphs List a few months back:
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When I was passing through the field of psychology,
I eventually came to write a program, "Theme One"
by name, that was designed to integrate a number
of prototypical aspects and selected functions
of inductive and deductive reasoning by basing
them on a "common denominator", as I called it,
that is to say, the LUB in an implicit lattice
of abstract graph-theoretic data structures --
but a surprising side-effect of this work was
that I learned a whole lot about the reasons
why "empircists" and "rationalists" have so
much trouble understanding each other, and
even when, or especially when, it is the
divergent sides of the very same thinker
that one discovers to be at issue here.
The deductive functions of my program are implemented
via a logical interpretation of the above-mentioned
abstract data structure that I developed from the
Alpha Layer of Peirce's Existential Graphs.
The inductive functions are built around a core utility
that consists of a "two-level formal language learner",
and which I applied at the time to problems in protocol
analysis and sequential data sets, while working within
a qualitative research paradigm. Here is an example of
the sort of dataset that I used it to explore and model,
presenting what follows in three parts:
1. The codebook that was used to code the videotaped sessions.
2. A raw coded data set of a single family interaction session.
3. A transcription of the raw data set into a logical summary,
consisting of a single proposition in the following form:
(( j1_f# j2_c# j3_q# j4_v# k1_f3 k2_c1 k3_q2 k4_v3
)( j1_f3 j2_c1 j3_q2 j4_v3 k1_f1 k2_c1 k3_q2 k4_v3
)( j1_f1 j2_c1 j3_q2 j4_v3 k1_f3 k2_c4 k3_q2 k4_v3
)( ...
)( j1_f1 j2_c1 j3_q2 j4_v3 k1_f3 k2_c1 k3_q2 k4_v3
))
This is a disjunction of conjunctive expressions, interpreted to describe
a set of ordered pairs, where each pair codes the state transition of the
parent-child dyad by telling what was happening at the first event of the
transition followed by what was happening at the second event of the pair.
The "j?_*" and "k?_*" codes describes the 1st and 2nd events, respectively.
Accordingly the above fragment says something like this:
| EITHER f#_start c##_start v#_start AND THEN
| f3_mother c12_talk v3_neutral_affect
| OR f3_mother c12_talk v3_neutral_affect AND THEN
| f1_child c12_talk v3_neutral_affect
| OR f1_child c12_talk v3_neutral_affect AND THEN
| f3_mother c42_command_ambiguous v3_neutral_affect
| OR ... ... ... AND THEN
| ...
| OR f1_child c12_talk v3_neutral_affect AND THEN
| f3_mother c12_talk v3_neutral_affect
| END OR.
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"Family Interaction Analysis" (FIA)
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"Family Interaction Data" (FID) Codes:
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f#_family_member
f1_child
f2_father
f3_mother
f4_older_brother
f5_older_sister
f6_younger_brother
f7_younger_sister
f8_household_pets
f9_multiple_recipients
f0_objects
c##_content
c1#_conversation
c11_positive_verbal
c12_talk
c13_negative_verbal
c2#_affiliate/distance
c21_endearment
c22_tease
c23_verbal_attack
c3#_clear_directive
c31_request
c32_command
c33_coerce
c4#_ambiguous_directive
c41_request_ambiguous
c42_command_ambiguous
c43_coerce_ambiguous
c5#_response_to_directive
c51_agree
c52
c53_refuse
c6#_vocal_behavior
c61
c62_vocal
c63
c7#_nonverbal_behavior
c71_positive_nonverbal
c72_neutral_nonverbal
c73_negative_nonverbal
c8#_low_grade_physical_contact
c81_touch
c82
c83_physical_aggression
c9#_pronounced_physical_interaction
c91_hold
c92_physical_interact
c93_physical_attack
c0#_compliance_behavior
c01_comply
c02
c03_noncomply
v#_valence
v1_exuberant_affect
v2_positive_affect
v3_neutral_affect
v4_negative_affect
v5_extreme_negative_affect
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"Family Interaction Transition" (FIT) Codes:
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j1_f*_family_member
j1_f#_null_value
j1_f1_child
j1_f2_father
j1_f3_mother
j2_c*_content
j2_c#_null_value
j2_c1_conversation
j2_c2_affiliate/distance
j2_c3_clear_directive
j2_c4_ambiguous_directive
j2_c5_response_to_directive
j2_c6_vocal_behavior
j2_c7_nonverbal_behavior
j2_c8_low_grade_physical_contact
j2_c9_pronounced_physical_interaction
j2_c0_compliance_behavior
j3_q*_quality
j3_q#_null_value
j3_q1_positive
j3_q2_neutral
j3_q3_negative
j4_v*_valence
j4_v#_null_value
j4_v1_exuberant_affect
j4_v2_positive_affect
j4_v3_neutral_affect
j4_v4_negative_affect
j4_v5_extreme_negative_affect
k1_f*_family_member
k1_f#_null_value
k1_f1_child
k1_f2_father
k1_f3_mother
k2_c*_content
k2_c#_null_value
k2_c1_conversation
k2_c2_affiliate/distance
k2_c3_clear_directive
k2_c4_ambiguous_directive
k2_c5_response_to_directive
k2_c6_vocal_behavior
k2_c7_nonverbal_behavior
k2_c8_low_grade_physical_contact
k2_c9_pronounced_physical_interaction
k2_c0_compliance_behavior
k3_q*_quality
k3_q#_null_value
k3_q1_positive
k3_q2_neutral
k3_q3_negative
k4_v*_valence
k4_v#_null_value
k4_v1_exuberant_affect
k4_v2_positive_affect
k4_v3_neutral_affect
k4_v4_negative_affect
k4_v5_extreme_negative_affect
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"Family Interaction Transitions, Observational Data" (FIT.OBS) File:
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TRL FAMILY SESSION FOCUS OBSERVER FAMILY MEMBERS MO/DY/YR HR:MN
1 MXYZ 1 1 22 13000000 12/03/86 12:58
0 -00100 0
0 99999 0
2 -00302 2
2 31213 5
2 11233 8
2 34213 10
2 33213 18
2 10133 19
2 14233 22
2 30113 24
2 99999 29
2 31113 40
2 11233 43
2 31212 46
2 11232 51
2 31213 54
2 11232 56
2 99999 61
2 11233 68
2 36213 70
2 33213 73
2 16232 74
2 33213 77
2 16232 78
2 31312 82
2 99999 91
2 11233 94
2 31213 96
2 99999 101
2 31112 103
2 11232 106
2 31213 108
2 11232 109
2 36212 112
2 16232 115
2 11232 120
2 31212 122
2 11232 127
2 16232 131
2 11232 136
2 16232 138
2 31213 143
2 11232 148
2 16232 155
2 31212 160
2 16232 168
2 31213 170
2 33213 175
2 10133 177
2 35113 184
2 31213 187
2 30113 189
2 11233 192
2 31213 194
2 11233 197
2 31213 200
2 11232 202
2 16232 205
2 99999 211
2 11232 214
2 31213 218
2 13233 222
2 35113 225
2 31213 227
2 11233 228
2 30113 230
2 11234 234
2 31212 238
2 33213 241
2 10133 242
2 31213 244
2 11232 245
2 31213 252
2 11233 254
2 31213 256
2 16233 267
2 11232 269
2 11231 278
2 34213 282
2 10133 287
2 31213 289
2 11232 291
2 31213 296
2 13133 301
2 35113 305
2 11233 309
2 31213 311
2 11233 313
2 31213 316
2 11233 319
2 31213 322
2 11233 323
2 31213 324
2 11233 326
2 33213 329
2 10133 331
2 11233 333
2 31112 338
2 11233 342
2 31213 344
2 11233 347
2 31213 349
2 11233 351
2 31213 352
2 16233 354
2 36212 356
2 11233 362
2 31213 367
2 11233 370
2 31213 371
2 11232 373
2 31212 378
2 11232 381
2 31213 382
2 11233 389
2 31213 392
2 34213 394
2 10133 396
2 31113 398
2 11233 401
2 31213 403
2 11233 405
2 31212 406
2 11233 409
2 31213 412
2 11233 414
2 31213 416
2 36212 417
2 16232 419
2 31312 422
2 33213 426
2 33213 430
2 10133 431
2 10133 434
2 31213 438
2 11233 439
2 31213 440
2 11233 441
2 31213 443
2 11233 449
2 31112 450
2 31212 455
2 16232 457
2 31213 462
2 11232 463
2 31212 467
2 16232 469
2 31213 473
2 11233 477
2 31213 479
2 11133 490
2 31113 492
2 31213 495
2 16232 514
2 31112 517
2 16232 524
2 11232 527
2 31213 530
2 16232 534
2 36212 537
2 32212 539
2 16232 544
2 31213 547
2 11233 548
2 31213 549
2 11232 553
2 99999 561
2 16212 564
2 31213 569
2 11232 575
2 31314 577
2 31213 585
2 16232 589
2 33213 591
2 10133 593
2 11233 595
2 31213 599
2 88888 603
0 -00500 605
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"Family Interaction Transitions, Logical Representation" (FIT.LOG) File:
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(( j1_f# j2_c# j3_q# j4_v# k1_f3 k2_c1 k3_q2 k4_v3
)( j1_f3 j2_c1 j3_q2 j4_v3 k1_f1 k2_c1 k3_q2 k4_v3
)( j1_f1 j2_c1 j3_q2 j4_v3 k1_f3 k2_c4 k3_q2 k4_v3
)( j1_f3 j2_c4 j3_q2 j4_v3 k1_f3 k2_c3 k3_q2 k4_v3
)( j1_f3 j2_c3 j3_q2 j4_v3 k1_f1 k2_c0 k3_q1 k4_v3
)( j1_f1 j2_c0 j3_q1 j4_v3 k1_f1 k2_c4 k3_q2 k4_v3
)( j1_f1 j2_c4 j3_q2 j4_v3 k1_f3 k2_c0 k3_q1 k4_v3
)( j1_f3 j2_c0 j3_q1 j4_v3 k1_f# k2_c# k3_q# k4_v#
)( j1_f# j2_c# j3_q# j4_v# k1_f3 k2_c1 k3_q1 k4_v3
)( j1_f3 j2_c1 j3_q1 j4_v3 k1_f1 k2_c1 k3_q2 k4_v3
)( j1_f1 j2_c1 j3_q2 j4_v3 k1_f3 k2_c1 k3_q2 k4_v2
)( j1_f3 j2_c1 j3_q2 j4_v2 k1_f1 k2_c1 k3_q2 k4_v2
)( j1_f1 j2_c1 j3_q2 j4_v2 k1_f3 k2_c1 k3_q2 k4_v3
)( j1_f3 j2_c1 j3_q2 j4_v3 k1_f1 k2_c1 k3_q2 k4_v2
)( j1_f1 j2_c1 j3_q2 j4_v2 k1_f# k2_c# k3_q# k4_v#
)( j1_f# j2_c# j3_q# j4_v# k1_f1 k2_c1 k3_q2 k4_v3
)( j1_f1 j2_c1 j3_q2 j4_v3 k1_f3 k2_c6 k3_q2 k4_v3
)( j1_f3 j2_c6 j3_q2 j4_v3 k1_f3 k2_c3 k3_q2 k4_v3
)( j1_f3 j2_c3 j3_q2 j4_v3 k1_f1 k2_c6 k3_q2 k4_v2
)( j1_f1 j2_c6 j3_q2 j4_v2 k1_f3 k2_c3 k3_q2 k4_v3
)( j1_f3 j2_c3 j3_q2 j4_v3 k1_f1 k2_c6 k3_q2 k4_v2
)( j1_f1 j2_c6 j3_q2 j4_v2 k1_f3 k2_c1 k3_q3 k4_v2
)( j1_f3 j2_c1 j3_q3 j4_v2 k1_f# k2_c# k3_q# k4_v#
)( j1_f# j2_c# j3_q# j4_v# k1_f1 k2_c1 k3_q2 k4_v3
)( j1_f1 j2_c1 j3_q2 j4_v3 k1_f3 k2_c1 k3_q2 k4_v3
)( j1_f3 j2_c1 j3_q2 j4_v3 k1_f# k2_c# k3_q# k4_v#
)( j1_f# j2_c# j3_q# j4_v# k1_f3 k2_c1 k3_q1 k4_v2
)( j1_f3 j2_c1 j3_q1 j4_v2 k1_f1 k2_c1 k3_q2 k4_v2
)( j1_f1 j2_c1 j3_q2 j4_v2 k1_f3 k2_c1 k3_q2 k4_v3
)( j1_f3 j2_c1 j3_q2 j4_v3 k1_f1 k2_c1 k3_q2 k4_v2
)( j1_f1 j2_c1 j3_q2 j4_v2 k1_f3 k2_c6 k3_q2 k4_v2
)( j1_f3 j2_c6 j3_q2 j4_v2 k1_f1 k2_c6 k3_q2 k4_v2
)( j1_f1 j2_c6 j3_q2 j4_v2 k1_f1 k2_c1 k3_q2 k4_v2
)( j1_f1 j2_c1 j3_q2 j4_v2 k1_f3 k2_c1 k3_q2 k4_v2
)( j1_f3 j2_c1 j3_q2 j4_v2 k1_f1 k2_c1 k3_q2 k4_v2
)( j1_f1 j2_c1 j3_q2 j4_v2 k1_f1 k2_c6 k3_q2 k4_v2
)( j1_f1 j2_c6 j3_q2 j4_v2 k1_f1 k2_c1 k3_q2 k4_v2
)( j1_f1 j2_c1 j3_q2 j4_v2 k1_f1 k2_c6 k3_q2 k4_v2
)( j1_f1 j2_c6 j3_q2 j4_v2 k1_f3 k2_c1 k3_q2 k4_v3
)( j1_f3 j2_c1 j3_q2 j4_v3 k1_f1 k2_c1 k3_q2 k4_v2
)( j1_f1 j2_c1 j3_q2 j4_v2 k1_f1 k2_c6 k3_q2 k4_v2
)( j1_f1 j2_c6 j3_q2 j4_v2 k1_f3 k2_c1 k3_q2 k4_v2
)( j1_f3 j2_c1 j3_q2 j4_v2 k1_f1 k2_c6 k3_q2 k4_v2
)( j1_f1 j2_c6 j3_q2 j4_v2 k1_f3 k2_c1 k3_q2 k4_v3
)( j1_f3 j2_c1 j3_q2 j4_v3 k1_f3 k2_c3 k3_q2 k4_v3
)( j1_f3 j2_c3 j3_q2 j4_v3 k1_f1 k2_c0 k3_q1 k4_v3
)( j1_f1 j2_c0 j3_q1 j4_v3 k1_f3 k2_c5 k3_q1 k4_v3
)( j1_f3 j2_c5 j3_q1 j4_v3 k1_f3 k2_c1 k3_q2 k4_v3
)( j1_f3 j2_c1 j3_q2 j4_v3 k1_f3 k2_c0 k3_q1 k4_v3
)( j1_f3 j2_c0 j3_q1 j4_v3 k1_f1 k2_c1 k3_q2 k4_v3
)( j1_f1 j2_c1 j3_q2 j4_v3 k1_f3 k2_c1 k3_q2 k4_v3
)( j1_f3 j2_c1 j3_q2 j4_v3 k1_f1 k2_c1 k3_q2 k4_v3
)( j1_f1 j2_c1 j3_q2 j4_v3 k1_f3 k2_c1 k3_q2 k4_v3
)( j1_f3 j2_c1 j3_q2 j4_v3 k1_f1 k2_c1 k3_q2 k4_v2
)( j1_f1 j2_c1 j3_q2 j4_v2 k1_f1 k2_c6 k3_q2 k4_v2
)( j1_f1 j2_c6 j3_q2 j4_v2 k1_f# k2_c# k3_q# k4_v#
)( j1_f# j2_c# j3_q# j4_v# k1_f1 k2_c1 k3_q2 k4_v2
)( j1_f1 j2_c1 j3_q2 j4_v2 k1_f3 k2_c1 k3_q2 k4_v3
)( j1_f3 j2_c1 j3_q2 j4_v3 k1_f1 k2_c3 k3_q2 k4_v3
)( j1_f1 j2_c3 j3_q2 j4_v3 k1_f3 k2_c5 k3_q1 k4_v3
)( j1_f3 j2_c5 j3_q1 j4_v3 k1_f3 k2_c1 k3_q2 k4_v3
)( j1_f3 j2_c1 j3_q2 j4_v3 k1_f1 k2_c1 k3_q2 k4_v3
)( j1_f1 j2_c1 j3_q2 j4_v3 k1_f3 k2_c0 k3_q1 k4_v3
)( j1_f3 j2_c0 j3_q1 j4_v3 k1_f1 k2_c1 k3_q2 k4_v4
)( j1_f1 j2_c1 j3_q2 j4_v4 k1_f3 k2_c1 k3_q2 k4_v2
)( j1_f3 j2_c1 j3_q2 j4_v2 k1_f3 k2_c3 k3_q2 k4_v3
)( j1_f3 j2_c3 j3_q2 j4_v3 k1_f1 k2_c0 k3_q1 k4_v3
)( j1_f1 j2_c0 j3_q1 j4_v3 k1_f3 k2_c1 k3_q2 k4_v3
)( j1_f3 j2_c1 j3_q2 j4_v3 k1_f1 k2_c1 k3_q2 k4_v2
)( j1_f1 j2_c1 j3_q2 j4_v2 k1_f3 k2_c1 k3_q2 k4_v3
)( j1_f3 j2_c1 j3_q2 j4_v3 k1_f1 k2_c1 k3_q2 k4_v3
)( j1_f1 j2_c1 j3_q2 j4_v3 k1_f3 k2_c1 k3_q2 k4_v3
)( j1_f3 j2_c1 j3_q2 j4_v3 k1_f1 k2_c6 k3_q2 k4_v3
)( j1_f1 j2_c6 j3_q2 j4_v3 k1_f1 k2_c1 k3_q2 k4_v2
)( j1_f1 j2_c1 j3_q2 j4_v2 k1_f1 k2_c1 k3_q2 k4_v1
)( j1_f1 j2_c1 j3_q2 j4_v1 k1_f3 k2_c4 k3_q2 k4_v3
)( j1_f3 j2_c4 j3_q2 j4_v3 k1_f1 k2_c0 k3_q1 k4_v3
)( j1_f1 j2_c0 j3_q1 j4_v3 k1_f3 k2_c1 k3_q2 k4_v3
)( j1_f3 j2_c1 j3_q2 j4_v3 k1_f1 k2_c1 k3_q2 k4_v2
)( j1_f1 j2_c1 j3_q2 j4_v2 k1_f3 k2_c1 k3_q2 k4_v3
)( j1_f3 j2_c1 j3_q2 j4_v3 k1_f1 k2_c3 k3_q1 k4_v3
)( j1_f1 j2_c3 j3_q1 j4_v3 k1_f3 k2_c5 k3_q1 k4_v3
)( j1_f3 j2_c5 j3_q1 j4_v3 k1_f1 k2_c1 k3_q2 k4_v3
)( j1_f1 j2_c1 j3_q2 j4_v3 k1_f3 k2_c1 k3_q2 k4_v3
)( j1_f3 j2_c1 j3_q2 j4_v3 k1_f1 k2_c1 k3_q2 k4_v3
)( j1_f1 j2_c1 j3_q2 j4_v3 k1_f3 k2_c1 k3_q2 k4_v3
)( j1_f3 j2_c1 j3_q2 j4_v3 k1_f1 k2_c1 k3_q2 k4_v3
)( j1_f1 j2_c1 j3_q2 j4_v3 k1_f3 k2_c1 k3_q2 k4_v3
)( j1_f3 j2_c1 j3_q2 j4_v3 k1_f1 k2_c1 k3_q2 k4_v3
)( j1_f1 j2_c1 j3_q2 j4_v3 k1_f3 k2_c1 k3_q2 k4_v3
)( j1_f3 j2_c1 j3_q2 j4_v3 k1_f1 k2_c1 k3_q2 k4_v3
)( j1_f1 j2_c1 j3_q2 j4_v3 k1_f3 k2_c3 k3_q2 k4_v3
)( j1_f3 j2_c3 j3_q2 j4_v3 k1_f1 k2_c0 k3_q1 k4_v3
)( j1_f1 j2_c0 j3_q1 j4_v3 k1_f1 k2_c1 k3_q2 k4_v3
)( j1_f1 j2_c1 j3_q2 j4_v3 k1_f3 k2_c1 k3_q1 k4_v2
)( j1_f3 j2_c1 j3_q1 j4_v2 k1_f1 k2_c1 k3_q2 k4_v3
)( j1_f1 j2_c1 j3_q2 j4_v3 k1_f3 k2_c1 k3_q2 k4_v3
)( j1_f3 j2_c1 j3_q2 j4_v3 k1_f1 k2_c1 k3_q2 k4_v3
)( j1_f1 j2_c1 j3_q2 j4_v3 k1_f3 k2_c1 k3_q2 k4_v3
)( j1_f3 j2_c1 j3_q2 j4_v3 k1_f1 k2_c1 k3_q2 k4_v3
)( j1_f1 j2_c1 j3_q2 j4_v3 k1_f3 k2_c1 k3_q2 k4_v3
)( j1_f3 j2_c1 j3_q2 j4_v3 k1_f1 k2_c6 k3_q2 k4_v3
)( j1_f1 j2_c6 j3_q2 j4_v3 k1_f3 k2_c6 k3_q2 k4_v2
)( j1_f3 j2_c6 j3_q2 j4_v2 k1_f1 k2_c1 k3_q2 k4_v3
)( j1_f1 j2_c1 j3_q2 j4_v3 k1_f3 k2_c1 k3_q2 k4_v3
)( j1_f3 j2_c1 j3_q2 j4_v3 k1_f1 k2_c1 k3_q2 k4_v3
)( j1_f1 j2_c1 j3_q2 j4_v3 k1_f3 k2_c1 k3_q2 k4_v3
)( j1_f3 j2_c1 j3_q2 j4_v3 k1_f1 k2_c1 k3_q2 k4_v2
)( j1_f1 j2_c1 j3_q2 j4_v2 k1_f3 k2_c1 k3_q2 k4_v2
)( j1_f3 j2_c1 j3_q2 j4_v2 k1_f1 k2_c1 k3_q2 k4_v2
)( j1_f1 j2_c1 j3_q2 j4_v2 k1_f3 k2_c1 k3_q2 k4_v3
)( j1_f3 j2_c1 j3_q2 j4_v3 k1_f1 k2_c1 k3_q2 k4_v3
)( j1_f1 j2_c1 j3_q2 j4_v3 k1_f3 k2_c1 k3_q2 k4_v3
)( j1_f3 j2_c1 j3_q2 j4_v3 k1_f3 k2_c4 k3_q2 k4_v3
)( j1_f3 j2_c4 j3_q2 j4_v3 k1_f1 k2_c0 k3_q1 k4_v3
)( j1_f1 j2_c0 j3_q1 j4_v3 k1_f3 k2_c1 k3_q1 k4_v3
)( j1_f3 j2_c1 j3_q1 j4_v3 k1_f1 k2_c1 k3_q2 k4_v3
)( j1_f1 j2_c1 j3_q2 j4_v3 k1_f3 k2_c1 k3_q2 k4_v3
)( j1_f3 j2_c1 j3_q2 j4_v3 k1_f1 k2_c1 k3_q2 k4_v3
)( j1_f1 j2_c1 j3_q2 j4_v3 k1_f3 k2_c1 k3_q2 k4_v2
)( j1_f3 j2_c1 j3_q2 j4_v2 k1_f1 k2_c1 k3_q2 k4_v3
)( j1_f1 j2_c1 j3_q2 j4_v3 k1_f3 k2_c1 k3_q2 k4_v3
)( j1_f3 j2_c1 j3_q2 j4_v3 k1_f1 k2_c1 k3_q2 k4_v3
)( j1_f1 j2_c1 j3_q2 j4_v3 k1_f3 k2_c1 k3_q2 k4_v3
)( j1_f3 j2_c1 j3_q2 j4_v3 k1_f3 k2_c6 k3_q2 k4_v2
)( j1_f3 j2_c6 j3_q2 j4_v2 k1_f1 k2_c6 k3_q2 k4_v2
)( j1_f1 j2_c6 j3_q2 j4_v2 k1_f3 k2_c1 k3_q3 k4_v2
)( j1_f3 j2_c1 j3_q3 j4_v2 k1_f3 k2_c3 k3_q2 k4_v3
)( j1_f3 j2_c3 j3_q2 j4_v3 k1_f3 k2_c3 k3_q2 k4_v3
)( j1_f3 j2_c3 j3_q2 j4_v3 k1_f1 k2_c0 k3_q1 k4_v3
)( j1_f1 j2_c0 j3_q1 j4_v3 k1_f1 k2_c0 k3_q1 k4_v3
)( j1_f1 j2_c0 j3_q1 j4_v3 k1_f3 k2_c1 k3_q2 k4_v3
)( j1_f3 j2_c1 j3_q2 j4_v3 k1_f1 k2_c1 k3_q2 k4_v3
)( j1_f1 j2_c1 j3_q2 j4_v3 k1_f3 k2_c1 k3_q2 k4_v3
)( j1_f3 j2_c1 j3_q2 j4_v3 k1_f1 k2_c1 k3_q2 k4_v3
)( j1_f1 j2_c1 j3_q2 j4_v3 k1_f3 k2_c1 k3_q2 k4_v3
)( j1_f3 j2_c1 j3_q2 j4_v3 k1_f1 k2_c1 k3_q2 k4_v3
)( j1_f1 j2_c1 j3_q2 j4_v3 k1_f3 k2_c1 k3_q1 k4_v2
)( j1_f3 j2_c1 j3_q1 j4_v2 k1_f3 k2_c1 k3_q2 k4_v2
)( j1_f3 j2_c1 j3_q2 j4_v2 k1_f1 k2_c6 k3_q2 k4_v2
)( j1_f1 j2_c6 j3_q2 j4_v2 k1_f3 k2_c1 k3_q2 k4_v3
)( j1_f3 j2_c1 j3_q2 j4_v3 k1_f1 k2_c1 k3_q2 k4_v2
)( j1_f1 j2_c1 j3_q2 j4_v2 k1_f3 k2_c1 k3_q2 k4_v2
)( j1_f3 j2_c1 j3_q2 j4_v2 k1_f1 k2_c6 k3_q2 k4_v2
)( j1_f1 j2_c6 j3_q2 j4_v2 k1_f3 k2_c1 k3_q2 k4_v3
)( j1_f3 j2_c1 j3_q2 j4_v3 k1_f1 k2_c1 k3_q2 k4_v3
)( j1_f1 j2_c1 j3_q2 j4_v3 k1_f3 k2_c1 k3_q2 k4_v3
)( j1_f3 j2_c1 j3_q2 j4_v3 k1_f1 k2_c1 k3_q1 k4_v3
)( j1_f1 j2_c1 j3_q1 j4_v3 k1_f3 k2_c1 k3_q1 k4_v3
)( j1_f3 j2_c1 j3_q1 j4_v3 k1_f3 k2_c1 k3_q2 k4_v3
)( j1_f3 j2_c1 j3_q2 j4_v3 k1_f1 k2_c6 k3_q2 k4_v2
)( j1_f1 j2_c6 j3_q2 j4_v2 k1_f3 k2_c1 k3_q1 k4_v2
)( j1_f3 j2_c1 j3_q1 j4_v2 k1_f1 k2_c6 k3_q2 k4_v2
)( j1_f1 j2_c6 j3_q2 j4_v2 k1_f1 k2_c1 k3_q2 k4_v2
)( j1_f1 j2_c1 j3_q2 j4_v2 k1_f3 k2_c1 k3_q2 k4_v3
)( j1_f3 j2_c1 j3_q2 j4_v3 k1_f1 k2_c6 k3_q2 k4_v2
)( j1_f1 j2_c6 j3_q2 j4_v2 k1_f3 k2_c6 k3_q2 k4_v2
)( j1_f3 j2_c6 j3_q2 j4_v2 k1_f3 k2_c2 k3_q2 k4_v2
)( j1_f3 j2_c2 j3_q2 j4_v2 k1_f1 k2_c6 k3_q2 k4_v2
)( j1_f1 j2_c6 j3_q2 j4_v2 k1_f3 k2_c1 k3_q2 k4_v3
)( j1_f3 j2_c1 j3_q2 j4_v3 k1_f1 k2_c1 k3_q2 k4_v3
)( j1_f1 j2_c1 j3_q2 j4_v3 k1_f3 k2_c1 k3_q2 k4_v3
)( j1_f3 j2_c1 j3_q2 j4_v3 k1_f1 k2_c1 k3_q2 k4_v2
)( j1_f1 j2_c1 j3_q2 j4_v2 k1_f# k2_c# k3_q# k4_v#
)( j1_f# j2_c# j3_q# j4_v# k1_f1 k2_c6 k3_q2 k4_v2
)( j1_f1 j2_c6 j3_q2 j4_v2 k1_f3 k2_c1 k3_q2 k4_v3
)( j1_f3 j2_c1 j3_q2 j4_v3 k1_f1 k2_c1 k3_q2 k4_v2
)( j1_f1 j2_c1 j3_q2 j4_v2 k1_f3 k2_c1 k3_q3 k4_v4
)( j1_f3 j2_c1 j3_q3 j4_v4 k1_f3 k2_c1 k3_q2 k4_v3
)( j1_f3 j2_c1 j3_q2 j4_v3 k1_f1 k2_c6 k3_q2 k4_v2
)( j1_f1 j2_c6 j3_q2 j4_v2 k1_f3 k2_c3 k3_q2 k4_v3
)( j1_f3 j2_c3 j3_q2 j4_v3 k1_f1 k2_c0 k3_q1 k4_v3
)( j1_f1 j2_c0 j3_q1 j4_v3 k1_f1 k2_c1 k3_q2 k4_v3
)( j1_f1 j2_c1 j3_q2 j4_v3 k1_f3 k2_c1 k3_q2 k4_v3
))
(( j1_f# ),( j1_f1 ),( j1_f3 ))
(( j2_c# ),( j2_c1 ),( j2_c2 ),( j2_c3 ),( j2_c4 ),( j2_c5 ),
( j2_c6 ),( j2_c7 ),( j2_c8 ),( j2_c9 ),( j2_c0 ))
(( j3_q# ),( j3_q1 ),( j3_q2 ),( j3_q3 ))
(( j4_v# ),( j4_v1 ),( j4_v2 ),( j4_v3 ),( j4_v4 ),( j4_v5 ))
((( j2_c7 )( j2_c8 )( j2_c9 )( j4_v5 )))
(( k1_f# ),( k1_f1 ),( k1_f3 ))
(( k2_c# ),( k2_c1 ),( k2_c2 ),( k2_c3 ),( k2_c4 ),( k2_c5 ),
( k2_c6 ),( k2_c7 ),( k2_c8 ),( k2_c9 ),( k2_c0 ))
(( k3_q# ),( k3_q1 ),( k3_q2 ),( k3_q3 ))
(( k4_v# ),( k4_v1 ),( k4_v2 ),( k4_v3 ),( k4_v4 ),( k4_v5 ))
((( k2_c7 )( k2_c8 )( k2_c9 )( k4_v5 )))
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