File size: 69,869 Bytes
6fa4bc9
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1088
1089
1090
1091
1092
1093
1094
1095
1096
1097
1098
1099
1100
1101
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1114
1115
1116
1117
1118
1119
1120
1121
1122
1123
1124
1125
1126
1127
1128
1129
1130
1131
1132
1133
1134
1135
1136
1137
1138
1139
1140
1141
1142
1143
1144
1145
1146
1147
1148
1149
1150
1151
1152
1153
1154
1155
1156
1157
1158
1159
1160
1161
1162
1163
1164
1165
1166
1167
1168
1169
1170
1171
1172
1173
1174
1175
1176
1177
1178
1179
1180
1181
1182
1183
1184
1185
1186
1187
1188
1189
1190
1191
1192
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1211
1212
1213
1214
1215
1216
1217
1218
1219
1220
1221
1222
1223
1224
1225
1226
1227
1228
1229
1230
1231
1232
1233
1234
1235
1236
1237
1238
1239
1240
1241
1242
1243
{
    "paper_id": "P89-1027",
    "header": {
        "generated_with": "S2ORC 1.0.0",
        "date_generated": "2023-01-19T08:14:44.067795Z"
    },
    "title": "OF LONG DISTANCE DEPENDENCIES IN LFG AND TAG: FUNCTIONAL UNCERTAINTY IN LFG IS A COROLLARY IN TAG\"",
    "authors": [
        {
            "first": "Aravind",
            "middle": [
                "K"
            ],
            "last": "Joshi",
            "suffix": "",
            "affiliation": {
                "laboratory": "",
                "institution": "University of Pennsylvania Philadelphia",
                "location": {
                    "postCode": "19104",
                    "region": "PA"
                }
            },
            "email": "joshi@linc.cis.upenn.edu"
        },
        {
            "first": "K",
            "middle": [],
            "last": "Vijay-Shanker",
            "suffix": "",
            "affiliation": {},
            "email": ""
        }
    ],
    "year": "",
    "venue": null,
    "identifiers": {},
    "abstract": "In this paper the functional uncertainty machinery in LFG is compared with the treatment of long distance dependencies in TAG. It is shown that the functional uncertainty machinery is redundant in TAG, i.e., what functional uncertainty accomplishes for LFG follows f~om the TAG formalism itself and some aspects of the linguistic theory instantiated in TAG. It is also shown that the analyses provided by the functional uncertainty machinery can be obtained without requiring power beyond mildly context-sensitive grammars. Some linguistic and computational aspects of these results have been briefly discussed also.",
    "pdf_parse": {
        "paper_id": "P89-1027",
        "_pdf_hash": "",
        "abstract": [
            {
                "text": "In this paper the functional uncertainty machinery in LFG is compared with the treatment of long distance dependencies in TAG. It is shown that the functional uncertainty machinery is redundant in TAG, i.e., what functional uncertainty accomplishes for LFG follows f~om the TAG formalism itself and some aspects of the linguistic theory instantiated in TAG. It is also shown that the analyses provided by the functional uncertainty machinery can be obtained without requiring power beyond mildly context-sensitive grammars. Some linguistic and computational aspects of these results have been briefly discussed also.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Abstract",
                "sec_num": null
            }
        ],
        "body_text": [
            {
                "text": "The so-called long distance dependencies are characterized in Lexical Functional Grammars (LFG) by the use of the formal device of functional uncertainty, as defined by Kaplan and Zaenan [3] and Kaplan and Maxwell [2] . In this paper, we relate this characterization to that provided by Tree ~,djoining Grammars (TAG), showing a direct correspondence between the functional uncertainty equations in LFG analyses and the elementary trees in TAGs that give analyses for \"long distance\" dependencies. We show that the functional uncertainty machinery is redundant in TAG, i.e., what functional uncertainty accomplishes for LFG follows from the TAG formalism itself and some fundamental aspects of the linguistic theory instantiated in TAG. We thus show that these analyses can be obtained without requiring power beyond mildly context-sensitive grammars. We also *This work was partially supported (for the first author) by the DRRPA grant N00014-85-K0018, AltO grant DAA29-84-9-0027, and NSF grant IRI84-10413-A02. The first author also benefited from some discussion with Mark Johnson and Ron Kaplan at the Titisee Workshop on Unification Grammars, March, 1988. briefly discuss the linguistic and computational significance of these results.",
                "cite_spans": [
                    {
                        "start": 169,
                        "end": 190,
                        "text": "Kaplan and Zaenan [3]",
                        "ref_id": null
                    },
                    {
                        "start": 195,
                        "end": 217,
                        "text": "Kaplan and Maxwell [2]",
                        "ref_id": null
                    },
                    {
                        "start": 1138,
                        "end": 1160,
                        "text": "Grammars, March, 1988.",
                        "ref_id": null
                    }
                ],
                "ref_spans": [],
                "eq_spans": [],
                "section": "INTRODUCTION",
                "sec_num": "1"
            },
            {
                "text": "Long distance phenomena are associated with the so-called movement. The following examples, 1. Mary Henry telephoned.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "INTRODUCTION",
                "sec_num": "1"
            },
            {
                "text": "2. Mary Bill said that Henry telephoned.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "INTRODUCTION",
                "sec_num": "1"
            },
            {
                "text": "telephoned.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Mary John claimed that Bill said that Henry",
                "sec_num": "3."
            },
            {
                "text": "illustrate the long distance dependencies due to topicalization, where the verb telephoned and its object Mary can be arbitrarily apart. It is difficult to state generalizations about these phenomena if one relies entirely on the surface structure (as defined in CFG based frameworks) since these phenomena cannot be localized at this level. Kaplan and Zaenan [3] note that, in LFG, rather than stating the generalizations on the c-structure, they must be stated on f-structures, since long distance dependencies are predicate argument dependencies, and such functional dependencies are represented in the f-structures. Thus, as stated in [2, 3] , in the sentences (1) , (2) , and (3) above, the dependencies are captured by the equations (in the LFG notation 1) by 1\" TOPIC =T OBJ, T TOPIC =T COMP OBJ, and 1\" TOPIC =T COMP COMP OBJ, respectively, which state that. the topic Mary is also the object of tele. phoned. In general, since any number of additional complement predicates may be introduced, these equations will have the general form \"f TOPIC =T COMP COMP ... OBJ Kaplan and Zaenen [3] introduced the formal device of functional unc'ertainty, in which this general case is stated by the equation",
                "cite_spans": [
                    {
                        "start": 360,
                        "end": 363,
                        "text": "[3]",
                        "ref_id": "BIBREF3"
                    },
                    {
                        "start": 639,
                        "end": 642,
                        "text": "[2,",
                        "ref_id": "BIBREF2"
                    },
                    {
                        "start": 643,
                        "end": 645,
                        "text": "3]",
                        "ref_id": "BIBREF3"
                    },
                    {
                        "start": 665,
                        "end": 668,
                        "text": "(1)",
                        "ref_id": "BIBREF0"
                    },
                    {
                        "start": 671,
                        "end": 674,
                        "text": "(2)",
                        "ref_id": "BIBREF2"
                    },
                    {
                        "start": 1075,
                        "end": 1096,
                        "text": "Kaplan and Zaenen [3]",
                        "ref_id": null
                    }
                ],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Mary John claimed that Bill said that Henry",
                "sec_num": "3."
            },
            {
                "text": "The functional uncertainty device restricts the labels (such as COMP \u00b0) to be drawn from the class of regular expressions. The definition of fstructures is extended to allow such equations [2, 3] . Informally, this definition states that if f is a f-structure and a is a regular set, then (fa) = v holds if the value of f for the attribute s is a fstructure fl such that (flY) --v holds, where sy is a string in a, or f = v and e E a.",
                "cite_spans": [
                    {
                        "start": 189,
                        "end": 192,
                        "text": "[2,",
                        "ref_id": "BIBREF2"
                    },
                    {
                        "start": 193,
                        "end": 195,
                        "text": "3]",
                        "ref_id": "BIBREF3"
                    }
                ],
                "ref_spans": [],
                "eq_spans": [],
                "section": "T TOPIC -T COMP\u00b0OBJ",
                "sec_num": null
            },
            {
                "text": "The functional uncertainty approach may be characterized as a localization of the long distance dependencies; a localization at the level of fstructures rather than at the level of c-structures. This illustrates the fact that if we use CFG-like rules to produce the surface structures, it is hard to state some generalizations directly; on the other hand, f-structures or elementary trees in TAGs (since they localize the predicate argument dependencies) are appropriate domains in which to state these generalizations. We show that there is a direct link between the regular expressions used in LFG and the elementary trees of TAG.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "T TOPIC -T COMP\u00b0OBJ",
                "sec_num": null
            },
            {
                "text": "In Section 2, we will define briefly the TAG formalism, describing some of the key points of the linguistic theory underlying it. We will also describe briefly Feature Structure Based Tree Adjoining Grammars (FTAG), and show how some elementary trees (auxiliary trees) behave as func: tions over feature structures. We will then show how regular sets over labels (such as COMP \u00b0) can also be denoted by functions over feature structures. In Section 3, we will consider the example of topicalization as it appears in Section 1 and show that the same statements are made by the two formalisms when we represent both the elementary trees of FTAG and functional uncertainties in LFG as functions over feature structures. We also point out some differences in the two analyses which arise due to the differences in the formalisms. In Section 4, we point out how these similar statements are stated differently in the two formalisms. The equations that capture the linguistic generalizations are still associated with individual rules (for the c-structure) of the grammar in LFG. Thus, in order to state generalizations for a phenomenon that is not localized in the cstructure, extra machinery such as functional uncertainty is needed. We show that what this extra machinery achieves for CFG based systems follows as a corollary of the TAG framework. This results from the fact that the elementary trees in a TAG provide an extended domain of locality, and factor out recursion and dependencies. A computational consequence of this result is that we can obtain these analyses without going outside the power of TAG and thus staying within the class of constrained grammatical formalisms characterized as mildly context.sensitive (Joshi [1] ). Another consequence of the differences in the representations (and localization) in the two formalisms is as follows. In a TAG, once an elementary tree is picked, there is no uncertainty about the functionality in long distance dependencies. Because LFG relies on a CFG framework, interactions between uncertainty equations can arise; the lack of such interactions in TAG can lead to simpler processing of long distance dependencies. Finally, we make some remarks as to the linguistic significance of restricting the use of regular sets in the functional uncertainty machinery by showing that the linguistic theory instantiated in TAG can predict that the path depicting the \"movement\" in long distance dependencies can be characterized by regular sets. (Figure 1 ) roughly correspond to \"simple sentences\". Thus, the root of an initial tree is labeled by S or ~. The frontier is all terminals. The auxiliary trees ( Figure 1 ) correspond roughly to minimal recursive constructions. Thus, if the root of an auxiliary tree is labeled by a nonterminal symbol, X, then there is a node (called the foot node) in the frontier which is labeled by X. The rest of the nodes in the frontier are labeled by terminal symbols.",
                "cite_spans": [
                    {
                        "start": 1723,
                        "end": 1733,
                        "text": "(Joshi [1]",
                        "ref_id": null
                    }
                ],
                "ref_spans": [
                    {
                        "start": 2491,
                        "end": 2500,
                        "text": "(Figure 1",
                        "ref_id": null
                    },
                    {
                        "start": 2654,
                        "end": 2662,
                        "text": "Figure 1",
                        "ref_id": null
                    }
                ],
                "eq_spans": [],
                "section": "I.I OUTLINE OF THE PAPER",
                "sec_num": null
            },
            {
                "text": "2We do not consider lexicalized TAGs (defined by Schabes, Abeille, and Joshi [7] ) which allow both adjoining and sub6titution. The ~uhs of this paper apply directly to them. Besides, they are formally equivalent to TAGs.",
                "cite_spans": [
                    {
                        "start": 77,
                        "end": 80,
                        "text": "[7]",
                        "ref_id": null
                    }
                ],
                "ref_spans": [],
                "eq_spans": [],
                "section": "I.I OUTLINE OF THE PAPER",
                "sec_num": null
            },
            {
                "text": "WP ' A I I P, V",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "~U p:",
                "sec_num": null
            },
            {
                "text": "Ag~m~ A~am~tm 2. The relation of T/to its descendants, i.e., the view from below. This feature structure is called b,.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "~U p:",
                "sec_num": null
            },
            {
                "text": "troo\u00a2 S X brooc \"-...~. ....... v J Aam.~p mat \u2022",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "~U p:",
                "sec_num": null
            },
            {
                "text": "We will now define the operation of adjoining. Consider the adjoining of/~ at the node marked with * in a. The subtree of a under the node marked with * is excised, and/3 is inserted in its place. Finally, the excised subtree is inserted below the foot node of w, as shown in Figure 1 .",
                "cite_spans": [],
                "ref_spans": [
                    {
                        "start": 276,
                        "end": 284,
                        "text": "Figure 1",
                        "ref_id": null
                    }
                ],
                "eq_spans": [],
                "section": "Figure 1: Elementary Trees in a TAG",
                "sec_num": null
            },
            {
                "text": "A more detailed description of TAGs and their linguistic relevance may be found in (Kroch and ao hi [51).",
                "cite_spans": [
                    {
                        "start": 83,
                        "end": 93,
                        "text": "(Kroch and",
                        "ref_id": null
                    }
                ],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Figure 1: Elementary Trees in a TAG",
                "sec_num": null
            },
            {
                "text": "2.1 FEATURE STRUCTURE BASED TREE ADJOINING GRAMMARS (FTAG)",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Figure 1: Elementary Trees in a TAG",
                "sec_num": null
            },
            {
                "text": "In unification grammars, a feature structure is associated with a node in a derivation tree in order to describe that node and its relation to features of other nodes in the derivation tree. In a FTAG, with each internal node, T/, we associate two feature structures (for details, see [9] ). These two feature structures capture the following relations (Figure 2) 1. The relation ofT/to its supertree, i.e., the view of the node from the top. The feature structure that describes this relationship is called ~. Note that both the t, and b, feature structures hold for the node 7. On the other hand, with each leaf node (either a terminal node or a foot node), 7, we associate only one feature structure (let us call it t,3).",
                "cite_spans": [
                    {
                        "start": 285,
                        "end": 288,
                        "text": "[9]",
                        "ref_id": null
                    }
                ],
                "ref_spans": [
                    {
                        "start": 353,
                        "end": 363,
                        "text": "(Figure 2)",
                        "ref_id": null
                    }
                ],
                "eq_spans": [],
                "section": "Figure 1: Elementary Trees in a TAG",
                "sec_num": null
            },
            {
                "text": "Let us now consider the case when adjoining takes place as shown in the Figure 2 . The notation we use is to write alongside each node, the t and b statements, with the t statement written above the b statement. Let us say that troo~,broot and tloot= bLoo~ are the t and b statements of the root and foot nodes of the auxiliary tree used for adjoining at the node 7. Based on what t and b stand for, it is obvious that on adjoining the statements t, and troot hold for the node corresponding to the root of the auxiliary tree. Similarly, the statements b, and b/oo~ hold for the node corresponding to the foot of the auxiliary tree. Thus, on adjoining, we unify t, with troot, and b, with b/oot. In fact, this adjoining-is permissible only if t.oo~ and t.",
                "cite_spans": [],
                "ref_spans": [
                    {
                        "start": 72,
                        "end": 80,
                        "text": "Figure 2",
                        "ref_id": "FIGREF0"
                    }
                ],
                "eq_spans": [],
                "section": "Figure 1: Elementary Trees in a TAG",
                "sec_num": null
            },
            {
                "text": "are compatible and so are b/oot and b~. If we do not adjoin at the node, 7, then we unify t, with b,. More details of the definition of FTAG may be found in [8, 9] .",
                "cite_spans": [
                    {
                        "start": 157,
                        "end": 160,
                        "text": "[8,",
                        "ref_id": null
                    },
                    {
                        "start": 161,
                        "end": 163,
                        "text": "9]",
                        "ref_id": null
                    }
                ],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Figure 1: Elementary Trees in a TAG",
                "sec_num": null
            },
            {
                "text": "We now give an example of an initial tree and an auxiliary tree in Figure 3 . We have shown only the necessary top and bottom feature structures for the relevant nodes. Also in each feature structure 3The linguistic relevance of this restriction has been discussed elsewhere (Kroch and Joshi [5] ). The general framework does not necessarily require it.",
                "cite_spans": [
                    {
                        "start": 275,
                        "end": 295,
                        "text": "(Kroch and Joshi [5]",
                        "ref_id": null
                    }
                ],
                "ref_spans": [
                    {
                        "start": 67,
                        "end": 75,
                        "text": "Figure 3",
                        "ref_id": "FIGREF1"
                    }
                ],
                "eq_spans": [],
                "section": "Figure 1: Elementary Trees in a TAG",
                "sec_num": null
            },
            {
                "text": "shown, we have only included those feature-value pairs that are relevant. For the auxiliary tree, we have labeled the root node S. We could have labeled it S with COMP and S as daughter nodes. These details are not relevant to the main point of the paper. We note that, just as in a TAG, the elementary trees which are the domains of dependencies are available as a single unit during each step of the derivation. For example, in al the topic and the object of the verb belong to the same tree (since this dependency has been factored into al) and are coindexed to specify the movemeat due to topicalization. In such cases, the dependencies between these nodes can be stated directly, avoiding the percolation of features during the derivation process as in string rewriting systems. Thus, these dependencies can be checked locally, and thus this checking need not be linked to the derivation process in an unbounded manner. to adjoining, since this feature structure is not known, we will treat it as a variable that gets instantiated on adjoining. This treatment can be formalized by treating the auxiliary trees as functions over feature structures (by A-abstracting the variable corresponding to the feature structure for the tree that will appear below the foot node). Adjoining corresponds to applying this function to the feature structure corresponding to the subtree below the node where adjoining takes place.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Figure 1: Elementary Trees in a TAG",
                "sec_num": null
            },
            {
                "text": "Treating adjoining as function application, where we consider auxiliary trees as functions, the representation of/3 is a function, say fz, of the form (see Figure 2) ~f. ($roo, A .. ",
                "cite_spans": [
                    {
                        "start": 170,
                        "end": 181,
                        "text": "($roo, A ..",
                        "ref_id": null
                    }
                ],
                "ref_spans": [
                    {
                        "start": 156,
                        "end": 165,
                        "text": "Figure 2)",
                        "ref_id": "FIGREF0"
                    }
                ],
                "eq_spans": [],
                "section": "Figure 1: Elementary Trees in a TAG",
                "sec_num": null
            },
            {
                "text": "If we now consider the tree 7 and the node T?, to allow the adjoining of/3 at the node ~, we must represent 7 by (...~. A f~(b.) A...)",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": ".(broot A f))",
                "sec_num": null
            },
            {
                "text": "Note that if we do not adjoin at ~7, since t, and /3, have to be unified, we must represent 7 by the formula (...~Ab~A...) which can be obtained by representing 7 by",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": ".(broot A f))",
                "sec_num": null
            },
            {
                "text": "In [8, 9], we have described a calculus, extending the logic developed by Rounds and Kasper [4, 6] , to encode the trees in a FTAG. We will very briefly describe this representation here.",
                "cite_spans": [
                    {
                        "start": 74,
                        "end": 95,
                        "text": "Rounds and Kasper [4,",
                        "ref_id": null
                    },
                    {
                        "start": 96,
                        "end": 98,
                        "text": "6]",
                        "ref_id": null
                    }
                ],
                "ref_spans": [],
                "eq_spans": [],
                "section": "A CALCULUS TO REPRESENT FTAG",
                "sec_num": "2.2"
            },
            {
                "text": "To understand the representation of adjoining, consider the trees given in Figure 2 , and in particular, the node rl. The feature structures associated with the node where adjoining takes place should reflect the feature structure after adjoining and as well as without adjoining. Further, the feature structure (corresponding to the tree structure below it) to be associated with the foot node is not known prior to adjoining, but becomes specified upon adjoining. Thus, the bottom feature structure associated with the foot node, which \"is b foot before adjoining, is instantiated on adjoining by unifying it with a feature structure for the tree that will finally appear below this node. Prior",
                "cite_spans": [],
                "ref_spans": [
                    {
                        "start": 75,
                        "end": 83,
                        "text": "Figure 2",
                        "ref_id": "FIGREF0"
                    }
                ],
                "eq_spans": [],
                "section": "A CALCULUS TO REPRESENT FTAG",
                "sec_num": "2.2"
            },
            {
                "text": "(...t~ A X(b~) A...)",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "A CALCULUS TO REPRESENT FTAG",
                "sec_num": "2.2"
            },
            {
                "text": "where I is the identity function. Similarly, we must allow adjoining by any auxiliary tree adjoinable at 7/(admissibility of adjoining is determined by the success or failure of unification). Thus, if /31,... ,/3, form the set of auxiliary trees, to allow for the possibility of adjoining by any auxiliary tree, as well as the possibility of no adjoining at a node, we must have a function, F, given by",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "A CALCULUS TO REPRESENT FTAG",
                "sec_num": "2.2"
            },
            {
                "text": "F = Af.(f~x(f) V... V f:~(f) V f)",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "A CALCULUS TO REPRESENT FTAG",
                "sec_num": "2.2"
            },
            {
                "text": "and then we represent 7 by",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "A CALCULUS TO REPRESENT FTAG",
                "sec_num": "2.2"
            },
            {
                "text": "In this way, we can represent the elementary trees (and hence the grammar) in an extended version of K-K logic (the extension consists of adding Aabstraction and application).",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "(. ..t, A F(b,) A .. .).",
                "sec_num": null
            },
            {
                "text": "We will now relate the analyses of long distance dependencies in LFG and TAG. For this purpose, we will focus our attention only on the dependencies due to topicalization, as illustrated by sentences 1, 2, and 3 in Section 1.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "TAG ANALYSES FOR LONG DISTANCE DE-PENDENCIES",
                "sec_num": null
            },
            {
                "text": "To facilitate our discussion, we will consider regular sets over labels (as used by the functional uncertainty machinery) as functions over feature structures (as we did for auxiliary trees in FTAG). In order to describe the representation of regular sets, we will treat all labels (attributes) as functions over feature structures. Thus, the label COMP, for example, is a function which given a value feature structure (say v) returns a feature structure denoted by COMP : v. Therefore, we can denote it by Av.COMP : v. In order to describe the representation of arbitrary regular sets we have to consider only their associated regular expressions. For example, COMP \u00b0 can be represented by the function C* which is the fixed-point 4 of",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "TAG ANALYSES FOR LONG DISTANCE DE-PENDENCIES",
                "sec_num": null
            },
            {
                "text": "F = Av.(F(COMP : v) V v) s",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "TAG ANALYSES FOR LONG DISTANCE DE-PENDENCIES",
                "sec_num": null
            },
            {
                "text": "Thus, the equation",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "TAG ANALYSES FOR LONG DISTANCE DE-PENDENCIES",
                "sec_num": null
            },
            {
                "text": "T TOPIC =T COMP*OBJ",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "TAG ANALYSES FOR LONG DISTANCE DE-PENDENCIES",
                "sec_num": null
            },
            {
                "text": "is satisfied by a feature structure that satisfies",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "TAG ANALYSES FOR LONG DISTANCE DE-PENDENCIES",
                "sec_num": null
            },
            {
                "text": "TOPIC : v A C* (OBJ : v).",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "TAG ANALYSES FOR LONG DISTANCE DE-PENDENCIES",
                "sec_num": null
            },
            {
                "text": "This feature structure will have a general form described by TOPIC : v A COMP : COMP : ... OBJ : v. Consider the FTAG fragment (as shown in Figure 3) which can be used to generate the sentences 1, 2, and 3 in Section 1. The initial tree al will be represented by cat : \"~ A F(topic : v A F(pred : telephonedAobj : v)). Ignoring some irrelevant details (such as the possibility of adjoining at nodes other than the S node), we cnn represent ax as",
                "cite_spans": [
                    {
                        "start": 91,
                        "end": 99,
                        "text": "OBJ : v.",
                        "ref_id": null
                    }
                ],
                "ref_spans": [
                    {
                        "start": 140,
                        "end": 146,
                        "text": "Figure",
                        "ref_id": null
                    }
                ],
                "eq_spans": [],
                "section": "TAG ANALYSES FOR LONG DISTANCE DE-PENDENCIES",
                "sec_num": null
            },
            {
                "text": "al = topic : v A F(obj : v)",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "TAG ANALYSES FOR LONG DISTANCE DE-PENDENCIES",
                "sec_num": null
            },
            {
                "text": "Turning our attention to /~h let us consider the bottom feature structure of the root of/~1. Since its COMP ~ the feature structure associated with the foot node (notice that no adjoining is allowed at the foot node and hence it has only one feature structure), and since adjoining can take place at the root node, we have the representation of 81 as where F is the function described in Section 2.2. From the point of view of the path from the root to the complement, the NP and VP nodes are irrelevant, so are any adjoinings on these nodes. So once again, if we discard the irrelevant information (from the point of view of comparing this analyses with the one in LFG), we can simplify the representation of 81 as",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "TAG ANALYSES FOR LONG DISTANCE DE-PENDENCIES",
                "sec_num": null
            },
            {
                "text": "As explained in Section 2.2, since j31 is the only auxiliary tree of interest, F would be defined as F = a/.Zl(/)v/.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Af.F(comp : f)",
                "sec_num": null
            },
            {
                "text": "Using the definition of/~1 above, and making some reductions we have",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Af.F(comp : f)",
                "sec_num": null
            },
            {
                "text": "F = Af.F(comp : f) V f",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Af.F(comp : f)",
                "sec_num": null
            },
            {
                "text": "This is exactly the same analysis as in LFG using the functional uncertainty machinery. Note that the fixed-point of F isC,. Now consider al. Obviously any structure derived from it can now be represented as",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Af.F(comp : f)",
                "sec_num": null
            },
            {
                "text": "topic : v A C * (obj : v)",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Af.F(comp : f)",
                "sec_num": null
            },
            {
                "text": "This is the same analysis as given by LFG.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Af.F(comp : f)",
                "sec_num": null
            },
            {
                "text": "In a TAG, the dependent items are part of the same elementary tree. Features of these nodes can be related locally within this elementary tree (as in a,). This relation is unaffected by any adjoinings on nodes of the elementary tree. Although the paths from the root to these dependent items are elaborated by the adjoinings, no external device (such as the functional uncertainty machinery) needs to be used to restrict the possible paths between the dependent nodes. For instance, in the example we have considered, the fact that TOPIC = COMP : COMP...",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Af.F(comp : f)",
                "sec_num": null
            },
            {
                "text": ": OBJ follows from the TAG framework itself. The regular path restrictions made in functional uncertainty statements such as in TOPIC = COMP*OBJ is redundant within the TAG framework.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Af.F(comp : f)",
                "sec_num": null
            },
            {
                "text": "We have compared LFG and TAG analyses of long distance dependencies, and have shown that what functional uncertainty does for LFG comes out as a corollary in TAG, without going beyond the power of mildly context sensitive grammars.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "COMPARISON OF THE TWO FORMALISMS",
                "sec_num": "4"
            },
            {
                "text": "Both approaches aim to localize long distance dependencies; the difference between TAG and LFG arises due to the domain of locality that the formalisms provide (i.e., the domain over which statements of dependencies can be stated within the formalisms).",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "COMPARISON OF THE TWO FORMALISMS",
                "sec_num": "4"
            },
            {
                "text": "In the LFG framework, CFG-like productions are used to build the c-structure. Equations are associated with these productions in order to build the f-structure. Since the long distance dependencies are localized at the functional level, additional machinery (functional uncertainty) is provided to capture this localization. In a TAG, the elementary trees, though used to build the \"phrase structure\" tree, also form the domain for localizing the functional dependencies. As a result, the long distance dependencies can be localized in the elementary trees. Therefore, such elementary trees tell us exactly where the filler \"moves\" (even in the case of such unbounded dependencies) and the functional uncertainty machinery is not necessary in the TAG framework. However, the functional uncertainty machinery makes explicit the predictions about the path between the \"moved\" argument (filler) and the predicate (which is close to the gap). In a TAG, this prediction is not explicit. Hence, as we have shown in the case of topicalization, the nature of elementary trees determines the derivation sequences allowed and we can confirm (as we have done in Section 3) that this prediction is the same as that made by the functional uncertainty machinery.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "COMPARISON OF THE TWO FORMALISMS",
                "sec_num": "4"
            },
            {
                "text": "The functional uncertainty machinery is a means by which infinite disjunctions can be specified in a finite manner. The reason that infinite number of disjunctions appear, is due to the fact that they correspond to infinite number of possible derivations. In a CFG based formalism, the checking of dependency cannot be separated from the derivation process. On the other hand, as shown in [9], since this separation is possible in TAG, only finite disjunctions are needed. In each elementary tree, there is no uncertainty about the kind of dependency between a filler and the position of the corresponding gap. Different dependencies correspond to different elementary trees. In this sense there is disjunction, but it is still only finite. Having picked one tree, there is no uncertainty about the grammatical function of the filler, no matter how many COMPs come in between due to adjoin-ing. This fact may have important consequences from the point of view of relative efficiency of processing of long distance dependencies in LFG and TAG. Consider, for example, the problem of interactions between two or more uncertainty equations in LFG as stated in [2] . Certain strings in COMP \u00b0 cannot be solutions for",
                "cite_spans": [
                    {
                        "start": 1156,
                        "end": 1159,
                        "text": "[2]",
                        "ref_id": "BIBREF2"
                    }
                ],
                "ref_spans": [],
                "eq_spans": [],
                "section": "INTERACTIONS AMONG UNCER-TAINTY EQUATIONS",
                "sec_num": "4.1"
            },
            {
                "text": "(f TOPIC) = (.f COMP\" GF)",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "INTERACTIONS AMONG UNCER-TAINTY EQUATIONS",
                "sec_num": "4.1"
            },
            {
                "text": "when this equation is conjoined (i.e., when it interacts) with (f COMP SUBJ NUM) = SING and (f TOPIC NUM) = PL. In this case, the shorter string COMP SUBJ cannot be used for COMP\" GF because of the interaction, although the strings COMP i SUB J, i >_ 2 can satisfy the above set of equations. In general, in LFG, extra work has to be done to account for interactions. On the other hand, in TAG, as we noted above, since there is no uncertainty about the grammatical function of the filler, such interactions do not arise at all.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "INTERACTIONS AMONG UNCER-TAINTY EQUATIONS",
                "sec_num": "4.1"
            },
            {
                "text": "From the definition of TAGs, it can be shown that the paths are always context-free sets [11] . If there are linguistic phenomena where the uncertainty machinery with regular sets is not enough, then the question arises whether TAG can provide an adequate analysis, given that paths are contextfree sets in TAGs. On the other hand, if regular sets are enough, we would like to explore whether the regularity requirement has a linguistic significance by itself. As far as we are aware, Kaplan and Zaenen [3] do not claim that the regularity requirement follows from the linguistic considerations. Rather, they have illustrated the adequacy of regular sets for the linguistic phenomena they have described. However, it appears that an appropriate linguistic theory instantiated in the TAG framework will justify the use of regular sets for the long distance phenomena considered here.",
                "cite_spans": [
                    {
                        "start": 89,
                        "end": 93,
                        "text": "[11]",
                        "ref_id": null
                    },
                    {
                        "start": 503,
                        "end": 506,
                        "text": "[3]",
                        "ref_id": "BIBREF3"
                    }
                ],
                "ref_spans": [],
                "eq_spans": [],
                "section": "REGULAR SETS IN FUNCTIONAL UNCERTAINTY",
                "sec_num": "4.2"
            },
            {
                "text": "To illustrate our claim, let us consider the elementary trees that are used in the TAG analysis of long distance dependencies. The elementary trees, Sl and/31 (given in Figure 3 ), are good representative examples of such trees. In the initial tree, \u00a2zt, the topic node is coindexed with the empty NP node that plays the grammatical role of object. At the functional level, this NP node is the object of the S node of oq (which is captured in the bottom feature structure associated with the S node). Hence, our representation of at (i.e., looking at it from the top) is given by topic : v A F(obj : v), capturing the \"movement\" due to topicalization. Thus, the path in the functional structure between the topic and the object is entirely determined by the function F, which in turn depends on the auxiliary trees that can be adjoined at the S node. These auxiliary trees, such as/~I, are those that introduce complementizer predicates. Auxiliary trees, in general, introduce modifiers or complementizer predicates as in/~1. (For our present discussion we can ignore the modifier type auxiliary trees). Auxiliary trees upon adjoining do not disturb the predicate argument structure of the tree to which they are adjoined. If we consider trees such as/~I, the complement is given by the tree that appears below the foot node. A principle of a linguistic theory instantiated in TAG (see [5] ), similar to the pro-jec~ion principle, predicts that the complement of the root (looking at it from below) is the feature structure associated with the foot node and (more importantly) this relation cannot be disrupted by any adjoinings. Thus, if we are given the feature structure, f, for the foot node (known only after adjoining), the bottom feature structure of the root can be specified as comp : jr, and that of the top feature structure of the root is F(comp : f), where F, as in a,, is used to account for adjoinings at the root.",
                "cite_spans": [
                    {
                        "start": 1386,
                        "end": 1389,
                        "text": "[5]",
                        "ref_id": null
                    }
                ],
                "ref_spans": [
                    {
                        "start": 169,
                        "end": 177,
                        "text": "Figure 3",
                        "ref_id": "FIGREF1"
                    }
                ],
                "eq_spans": [],
                "section": "REGULAR SETS IN FUNCTIONAL UNCERTAINTY",
                "sec_num": "4.2"
            },
            {
                "text": "To summarize, in al, the functional dependency between the topic and object nodes is entirely determined by the root and foot nodes of auxiliary trees that can be adjoined at the S node (the effect of using the function F). By examining such auxiliary trees, we have characterized the latter path as Af.F(comp : f). In grammatical terms, the path depicted by F can be specified by rightlinear productions F -* F comp : / I Since right-linear grammars generate only regular sets, and TAGs predict the use of such right-linear rules for the description of the paths, as just shown above, we can thus state that TAGs give a justification for the use of regular expressions in the functional uncertainty machinery.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "REGULAR SETS IN FUNCTIONAL UNCERTAINTY",
                "sec_num": "4.2"
            },
            {
                "text": "We will now show that what functional uncertainty accomplishes for LFG can be achieved within the FTAG framework without requiring power beyond that of TAGs. FTAG, as described in this paper, is unlimited in its generative capacity. By placing no restrictions on the feature structures associated with the nodes of elementary trees, it is possible to generate any recursively enumerable language. In [9], we have defined a restricted version of FTAG, called RFTAG, that can generate only TALs (the languages generated by TAGs). In RFTAG, we insist that the feature structures that are associated with nodes are bounded in size, a requirement similar to the finite closure membership restriction in GPSG. This restricted system will not allow us to give the analysis for the long distance dependencies due to topicalization (as given in the earlier sections), since we use the COMP attribute whose value cannot be bounded in size. However, it is possible to extend RFTAG in a certain way such that such analysis can be given. This extension of RFTAG still does not go beyond TAG and thus is within the class of mildly context-sensitive grammar formalisms defined by Joshi [1] . This extension of RFTAG is discussed in [10] .",
                "cite_spans": [
                    {
                        "start": 1171,
                        "end": 1174,
                        "text": "[1]",
                        "ref_id": "BIBREF0"
                    },
                    {
                        "start": 1217,
                        "end": 1221,
                        "text": "[10]",
                        "ref_id": null
                    }
                ],
                "ref_spans": [],
                "eq_spans": [],
                "section": "GENERATIVE CAPACITY AND LONG DISTANCE DEPENDENCY",
                "sec_num": "4.3"
            },
            {
                "text": "To give an informal idea of this extension and a justification for the above argument, let us consider the auxiliary tree,/~1 in Figure 3 . Although we coindex the value of the comp feature in the feature structure of the root node of/~1 with the feature structure associated with the foot node, we should note that this coindexing does not affect the context-freeness of derivation. Stated differently, the adjoining sequence at the root is independent of other nodes in the tree in spite of the coindexing. This is due to the fact that as the feature structure of the foot of/~1 gets instantiated on adjoining, this value is simply substituted (and not unified) for the value of the comp feature of the root node. Thus, the comp feature is being used just as any other feature that can be used to give tree addresses (except that comp indicates dominance at the functional level rather than at the tree structure level). In [10], we have formalized this notion by introducing graph adjoining grammars which generate exactly the same languages as TAGs. In a graph adjoining grammar, /~x is represented as shown in Figure 4 . Notice that in this representation the comp feature is like the features 1 and 2 (which indicate the left and right daughters of a node) and therefore not used explicitly.",
                "cite_spans": [],
                "ref_spans": [
                    {
                        "start": 129,
                        "end": 137,
                        "text": "Figure 3",
                        "ref_id": "FIGREF1"
                    },
                    {
                        "start": 1115,
                        "end": 1123,
                        "text": "Figure 4",
                        "ref_id": null
                    }
                ],
                "eq_spans": [],
                "section": "GENERATIVE CAPACITY AND LONG DISTANCE DEPENDENCY",
                "sec_num": "4.3"
            },
            {
                "text": "We have shown that for the treatment of long distance dependencies in TAG, the functional un- certainty machinery in LFG is redundant. We have also shown that the analyses provided by the functional uncertainty machinery can be obtained without going beyond the power of mildly context-sensitive grammars. We have briefly discussed some linguistic and computational aspects of these results. We believe that our results described in this paper can be extended to other formalisms, such as Combinatory Categorial Grammars (CCG), which also provide an e~ended domain of locality. It is of particular interest to carry out this investigation in the context of CCG because of their weak equivalence to TAG (Weir and Joshi [12] ). This exploration will help us view this equivalence from the structural point of view.",
                "cite_spans": [
                    {
                        "start": 702,
                        "end": 722,
                        "text": "(Weir and Joshi [12]",
                        "ref_id": null
                    }
                ],
                "ref_spans": [],
                "eq_spans": [],
                "section": "CONCLUSION",
                "sec_num": "5"
            },
            {
                "text": "Because of lack of space, we will not define the LFG notation. We assume that the reader is familiar with it.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "",
                "sec_num": null
            }
        ],
        "back_matter": [],
        "bib_entries": {
            "BIBREF0": {
                "ref_id": "b0",
                "title": "How much context-sensitivity is necessary for characterizing structural descriptions --Tree Adjoining Grammars",
                "authors": [
                    {
                        "first": "A",
                        "middle": [
                            "K"
                        ],
                        "last": "Joshi",
                        "suffix": ""
                    }
                ],
                "year": null,
                "venue": "",
                "volume": "",
                "issue": "",
                "pages": "",
                "other_ids": {},
                "num": null,
                "urls": [],
                "raw_text": "A. K. Joshi. How much context-sensitivity is necessary for characterizing structural de- scriptions --Tree Adjoining Grammars. In D.",
                "links": null
            },
            "BIBREF1": {
                "ref_id": "b1",
                "title": "Natural Language Processing q Theoretical, Computational and Psychological Perspective",
                "authors": [
                    {
                        "first": "L",
                        "middle": [],
                        "last": "Dowty",
                        "suffix": ""
                    },
                    {
                        "first": "A",
                        "middle": [],
                        "last": "Karttunen",
                        "suffix": ""
                    },
                    {
                        "first": "",
                        "middle": [],
                        "last": "Zwicky",
                        "suffix": ""
                    }
                ],
                "year": 1983,
                "venue": "",
                "volume": "",
                "issue": "",
                "pages": "",
                "other_ids": {},
                "num": null,
                "urls": [],
                "raw_text": "Dowty, L. Karttunen, and A. Zwicky, editors, Natural Language Processing q Theoretical, Computational and Psychological Perspective, Cambridge University Press, New York, NY, 1985. Originally presented in 1983.",
                "links": null
            },
            "BIBREF2": {
                "ref_id": "b2",
                "title": "An algorithm for functional uncertainity",
                "authors": [
                    {
                        "first": "R",
                        "middle": [
                            "M"
                        ],
                        "last": "Kaplan",
                        "suffix": ""
                    },
                    {
                        "first": "J",
                        "middle": [
                            "T"
                        ],
                        "last": "Maxwell",
                        "suffix": ""
                    }
                ],
                "year": 1988,
                "venue": "12 th International Conference on Comput. Ling",
                "volume": "",
                "issue": "",
                "pages": "",
                "other_ids": {},
                "num": null,
                "urls": [],
                "raw_text": "R. M. Kaplan and J. T. Maxwell. An al- gorithm for functional uncertainity. In 12 th International Conference on Comput. Ling., 1988.",
                "links": null
            },
            "BIBREF3": {
                "ref_id": "b3",
                "title": "Long distance dependencies,constituent structure, and functional uncertainity",
                "authors": [
                    {
                        "first": "R",
                        "middle": [
                            "M"
                        ],
                        "last": "Kaplan",
                        "suffix": ""
                    },
                    {
                        "first": "A",
                        "middle": [],
                        "last": "Zaenen",
                        "suffix": ""
                    }
                ],
                "year": 1988,
                "venue": "Alternative Conceptions of Phrase Structure",
                "volume": "",
                "issue": "",
                "pages": "",
                "other_ids": {},
                "num": null,
                "urls": [],
                "raw_text": "R. M. Kaplan and A. Zaenen. Long distance dependencies,constituent structure, and func- tional uncertainity. In M. Baltin and A. Kroch, editors, Alternative Conceptions of Phrase Structure, Chicago University Press, Chicago. IL, 1988.",
                "links": null
            },
            "BIBREF4": {
                "ref_id": "b4",
                "title": "A logical semantics for feature structures",
                "authors": [
                    {
                        "first": "R",
                        "middle": [],
                        "last": "Kasper",
                        "suffix": ""
                    },
                    {
                        "first": "W",
                        "middle": [
                            "C"
                        ],
                        "last": "Rounds",
                        "suffix": ""
                    }
                ],
                "year": 1986,
                "venue": "24 th meeting Assoc",
                "volume": "",
                "issue": "",
                "pages": "",
                "other_ids": {},
                "num": null,
                "urls": [],
                "raw_text": "R. Kasper and W. C. Rounds. A logical se- mantics for feature structures. In 24 th meet- ing Assoc. Comput. Ling., 1986.",
                "links": null
            },
            "BIBREF5": {
                "ref_id": "b5",
                "title": "Linguistic Relevance of Tree Adjoining Grammars",
                "authors": [
                    {
                        "first": "A",
                        "middle": [],
                        "last": "Kroch",
                        "suffix": ""
                    },
                    {
                        "first": "A",
                        "middle": [
                            "K"
                        ],
                        "last": "Joshi",
                        "suffix": ""
                    }
                ],
                "year": 1985,
                "venue": "",
                "volume": "",
                "issue": "",
                "pages": "",
                "other_ids": {},
                "num": null,
                "urls": [],
                "raw_text": "A. Kroch and A.K. Joshi. Linguistic Rele- vance of Tree Adjoining Grammars. Technical Report MS-CIS-85-18, Department of Com- puter and Information Science, University of Pennsylvania, Philadelphia, 1985. to appear in Linguistics and Philosophy, 1989.",
                "links": null
            },
            "BIBREF6": {
                "ref_id": "b6",
                "title": "A complete logical calculus for record structures representing linguistic information",
                "authors": [
                    {
                        "first": "W",
                        "middle": [
                            "C"
                        ],
                        "last": "Rounds",
                        "suffix": ""
                    },
                    {
                        "first": "R",
                        "middle": [],
                        "last": "Kasper",
                        "suffix": ""
                    }
                ],
                "year": 1986,
                "venue": "IEEE Symposium on Logic and Computer Science",
                "volume": "",
                "issue": "",
                "pages": "",
                "other_ids": {},
                "num": null,
                "urls": [],
                "raw_text": "W. C. Rounds and R. Kasper. A complete logical calculus for record structures repre- senting linguistic information. In IEEE Sym- posium on Logic and Computer Science, 1986.",
                "links": null
            },
            "BIBREF7": {
                "ref_id": "b7",
                "title": "New parsing strategies for tree adjoining grammars",
                "authors": [
                    {
                        "first": "Y",
                        "middle": [],
                        "last": "Schabes",
                        "suffix": ""
                    },
                    {
                        "first": "A",
                        "middle": [],
                        "last": "Abeille",
                        "suffix": ""
                    },
                    {
                        "first": "A",
                        "middle": [
                            "K"
                        ],
                        "last": "Joshi",
                        "suffix": ""
                    }
                ],
                "year": 1988,
                "venue": "12 th International Conference on Assoc. Comput. Ling",
                "volume": "",
                "issue": "",
                "pages": "",
                "other_ids": {},
                "num": null,
                "urls": [],
                "raw_text": "Y. Schabes, A. Abeille, and A. K. Joshi. New parsing strategies for tree adjoining gram- mars. In 12 th International Conference on Assoc. Comput. Ling., 1988.",
                "links": null
            },
            "BIBREF8": {
                "ref_id": "b8",
                "title": "A Study of Tee Adjoining Grammars",
                "authors": [
                    {
                        "first": "K",
                        "middle": [],
                        "last": "Vijayashanker",
                        "suffix": ""
                    }
                ],
                "year": 1987,
                "venue": "",
                "volume": "",
                "issue": "",
                "pages": "",
                "other_ids": {},
                "num": null,
                "urls": [],
                "raw_text": "K. Vijayashanker. A Study of Tee Adjoining Grammars. PhD thesis, University of Penn- sylvania, Philadelphia, Pa, 1987.",
                "links": null
            },
            "BIBREF9": {
                "ref_id": "b9",
                "title": "Feature structure based tree adjoining grammars",
                "authors": [
                    {
                        "first": "K",
                        "middle": [],
                        "last": "Vijay-Shanker",
                        "suffix": ""
                    },
                    {
                        "first": "A",
                        "middle": [
                            "K"
                        ],
                        "last": "Joshi",
                        "suffix": ""
                    }
                ],
                "year": 1988,
                "venue": "12 th International Conference on Comput. Ling",
                "volume": "",
                "issue": "",
                "pages": "",
                "other_ids": {},
                "num": null,
                "urls": [],
                "raw_text": "K. Vijay-Shanker and A. K. Joshi. Fea- ture structure based tree adjoining grammars. In 12 th International Conference on Comput. Ling., 1988.",
                "links": null
            },
            "BIBREF10": {
                "ref_id": "b10",
                "title": "Unification based approach to tree adjoining grammar",
                "authors": [
                    {
                        "first": "K",
                        "middle": [],
                        "last": "Vijay-Shanker",
                        "suffix": ""
                    },
                    {
                        "first": "A",
                        "middle": [
                            "K"
                        ],
                        "last": "Joshi",
                        "suffix": ""
                    }
                ],
                "year": 1989,
                "venue": "",
                "volume": "",
                "issue": "",
                "pages": "",
                "other_ids": {},
                "num": null,
                "urls": [],
                "raw_text": "K. Vijay-Shanker and A.K. Joshi. Unification based approach to tree adjoining grammar. 1989. forthcoming.",
                "links": null
            },
            "BIBREF11": {
                "ref_id": "b11",
                "title": "Characterizing structural descriptions produced by various grammatical formalisms",
                "authors": [
                    {
                        "first": "K",
                        "middle": [],
                        "last": "Vijay-Shanker",
                        "suffix": ""
                    },
                    {
                        "first": "D",
                        "middle": [
                            "J"
                        ],
                        "last": "Weir",
                        "suffix": ""
                    },
                    {
                        "first": "A",
                        "middle": [
                            "K"
                        ],
                        "last": "Joshi",
                        "suffix": ""
                    }
                ],
                "year": 1987,
                "venue": "25 th meeting Assoc. Comput. Ling",
                "volume": "",
                "issue": "",
                "pages": "",
                "other_ids": {},
                "num": null,
                "urls": [],
                "raw_text": "K. Vijay-Shanker, D. J. Weir, and A. K. Joshi. Characterizing structural descriptions produced by various grammatical formalisms. In 25 th meeting Assoc. Comput. Ling., 1987.",
                "links": null
            },
            "BIBREF12": {
                "ref_id": "b12",
                "title": "Combinatory categorial grammars: generative power and relationship to linear context-free rewriting systems",
                "authors": [
                    {
                        "first": "D",
                        "middle": [
                            "J"
                        ],
                        "last": "Weir",
                        "suffix": ""
                    },
                    {
                        "first": "A",
                        "middle": [
                            "K"
                        ],
                        "last": "Joshi",
                        "suffix": ""
                    }
                ],
                "year": 1988,
                "venue": "26 ta meeting Assoc. Comput. Ling",
                "volume": "",
                "issue": "",
                "pages": "",
                "other_ids": {},
                "num": null,
                "urls": [],
                "raw_text": "D. J. Weir and A. K. Joshi. Combinatory cat- egorial grammars: generative power and rela- tionship to linear context-free rewriting sys- tems. In 26 ta meeting Assoc. Comput. Ling., 1988.",
                "links": null
            }
        },
        "ref_entries": {
            "FIGREF0": {
                "uris": null,
                "text": "Feature Structures and Adjoining",
                "num": null,
                "type_str": "figure"
            },
            "FIGREF1": {
                "uris": null,
                "text": "Example of Feature Structures Associated with Elementary Trees",
                "num": null,
                "type_str": "figure"
            },
            "FIGREF2": {
                "uris": null,
                "text": "tin [8], we have established that the fixed-point exists. aWe use the fact that R\" = R'RU {e}. aLf(comp : f ^ s~bj : (...) ^...)",
                "num": null,
                "type_str": "figure"
            },
            "FIGREF3": {
                "uris": null,
                "text": "Figure 4: An Elementary DAG",
                "num": null,
                "type_str": "figure"
            }
        }
    }
}