kylelovesllms/grammar-v3-frames

Grammar V3 (determiners and PPs): Depth-1 Syntactic Frames

All syntactic frames with at most one relative clause generated by Grammar V3, the paired Head Initial / Head Final CFG with subject-verb number agreement, optional determiners and prepositional phrases of the translation-syntax project (experiments/03_grammar_v3/src/cfg_v3/grammar.py). The grammar is Grammar V2 with PPs adjoined to NP: NP -> N PP and PP -> P DP in Head Initial, NP -> PP N and PP -> DP P in Head Final. The PP moves in front of the noun it modifies, inside that noun's DP, and the preposition becomes a postposition: the dog near a cat chases this bird translates to the a cat near dog this bird chases.

PPs attach only to the subject and the object of the matrix clause. A noun takes at most one modifier (a PP or a relative clause), and the nouns inside a PP or a relative clause take none. The 1336 frames without a PP are the frames of Grammar V2.

The lexicon is Grammar V2's (26 nouns, 26 intransitive and 26 transitive verbs in both numbers, 26 adverbs, the determiners this, a, these, the and the complementizer that) with 26 prepositions: near, behind, beside, above, below, under, over, beyond, around, against, among, beneath, underneath, by, past, opposite, toward, with, without, alongside, before, after, between, inside, outside, atop.

Frames are category-level skeletons to be populated with lexical items; terminals carry their 1-based HI linear position (e.g. [N_pl_1]), so HF frames show where each HI slot moved. The populated datasets are grammar-v3-frames-ce-rb, grammar-v3-frames-ce and grammar-v3-frames-rb.

6744 frames (2440 ambiguous / in distribution, 4304 unambiguous / out of distribution; the number variants of 604 number-erased frames), each expanded into a copy row (HF Frame = HI Frame, the copy target) and a translate row (HF Frame = hierarchical translation), giving 13488 rows in frames.csv.

Columns

is_ambiguous is True iff the linear rule gives the hierarchical translation. The linear rule splits the frame at the first verb and emits each half with its determiners first, in source order, followed by its other words reversed; a preposition is reversed like any other word. Ambiguous frames are translated in training; unambiguous frames are copied in training and translated only at test. A frame whose only modifiers are PPs is ambiguous. first_divergence is the 1-based output position of the first word on which the linear rule and the hierarchical translation differ (empty if ambiguous).

fits_mixed, fits_that_aware_pivot and fits_prefix_copy make the same comparison for three other rules. Mixed: the linear procedure split at the matrix verb. That-aware pivot: split at the first verb that does not directly follow that. Prefix copy: the words before the first verb are copied verbatim; it fails on every frame with a PP on the subject.

Tier is ID (in distribution) for ambiguous frames, T1 for Subject / Subject Gap, T2 for Object / Object Gap and T3 for Subject / Object Gap. No pivot rule translates a frame of T2 or T3.

PP Site lists the arguments of the matrix clause that carry a PP: no-PP, subject, object or subject+object.

Determiners lists the nouns that carry a determiner (subject, object, subject-PP and object-PP = the noun of the PP on that argument, RC = the noun inside the relative clause). Determiner Condition groups them: no-determiner, matrix (only nouns outside the relative clause), RC (only the noun inside the RC) and matrix-RC (both).

Matrix Number is the number of the matrix subject, RC Number that of the noun the RC verb agrees with (None without an RC), and n_attractors counts nouns of the other number between a verb and the noun it agrees with (the noun of a PP on the subject, or the nouns of a center-embedded RC).

Counts per Category (frames, before task expansion)

Attachment Site	Gap Type	Frames	Ambiguous	Unambiguous
None	None	840	840	0
Subject	Subject Gap	1680	0	1680
Subject	Object Gap	1344	0	1344
Object	Subject Gap	1600	1600	0
Object	Object Gap	1280	0	1280
Total		6744	2440	4304

Frames per PP Site, and the frames each rule translates correctly

Attachment Site	Gap Type	Tier	PP Site	Frames	Linear	Mixed	That-aware pivot	Prefix copy	Example
None	None	ID	no-PP	40	40	40	40	40	the cat pursues this dog
None	None	ID	subject	160	160	160	160	0	the cat near this dog pursues a bird
None	None	ID	object	128	128	128	128	128	the cat pursues this dog near a bird
None	None	ID	subject+object	512	512	512	512	0	the cat near this dog pursues a bird behind the monkey
Subject	Subject Gap	T1	no-PP	400	0	400	400	0	the cat that swims pursues this dog
Subject	Subject Gap	T1	object	1280	0	1280	1280	0	the cat that swims pursues this dog near a bird
Subject	Object Gap	T3	no-PP	320	0	0	0	0	the cat that this dog pursues hugs a bird
Subject	Object Gap	T3	object	1024	0	0	0	0	the cat that this dog pursues hugs a bird near the monkey
Object	Subject Gap	ID	no-PP	320	320	320	320	320	the cat pursues this dog that swims
Object	Subject Gap	ID	subject	1280	1280	1280	1280	0	the cat near this dog pursues a bird that swims
Object	Object Gap	T2	no-PP	256	0	0	0	0	the cat pursues this dog that a bird hugs
Object	Object Gap	T2	subject	1024	0	0	0	0	the cat near this dog pursues a bird that the monkey hugs
Total				6744	2440	4120	4120	488

Frames per Determiner Condition

Attachment Site	Gap Type	Tier	no-determiner	matrix	RC	matrix-RC	Frames
None	None	ID	84	756	0	0	840
Subject	Subject Gap	T1	168	840	112	560	1680
Subject	Object Gap	T3	112	560	112	560	1344
Object	Subject Gap	ID	144	816	96	544	1600
Object	Object Gap	T2	96	544	96	544	1280
Total			604	3516	416	2208	6744