SlowGuess/ACL_2020_OCR huggingface dataset:
- superlative: operations involving max,min or other comparison operation to get the lowest or highest value. Sentence: xxx is the tallest player in xxx team.
- only: operation to identify the single entity which has a unique property the other entries do not have. Sentence: xxx is the only person to win all the games.
- before/after: operations to compare time or spatial order. Sentence: xxx is born before xxx.
- count: operations to enumerate the amount of entries meeting certain criterion. Sentence: there are two people from the central united states.
- comparison: operations to compare two or given number of entities. Sentence: xxx has better income than xxx.
- both/neither: operations to summarize the common properties of two entries. Sentence: xxx and xxx are both from the same country.
- sum/diff: operations to perform numeric summation or difference between numbers. Sentence: xxx gives 1 more dollars than xxxx in the donation.
- average: the average number of people attending the game is 500.
- unique: the uniq operation in sql to assemble summarize different entities. Sentence: from the table, players are from 4 unique countries.
C Semantic Parser
Specifically, the scorer is realized by a matching model  $f_{\gamma}$ , which takes a logic form  $P$  and the statement  $Y$  to output a consistency score  $f_{\gamma}(P,Y)$  between range of [0,1] with higher value indicating better consistency. As no groundtruth logical forms are provided, we utilize weakly supervised training. The set of logical forms generated is denoted as  $\mathbf{P}$ , the logical forms returning binary value of True is viewed as pseudo positive example  $\mathbf{P}^{+}$  and the logical forms returning False is treated as pseudo negative example  $\mathbf{P}^{-}$ . We propose to optimize the following objective to discriminate two sets:
$$
\operatorname * {a r g m a x} _ {\gamma} \underset {(\mathbf {T}, Y) \in D _ {t r a i n}} {\mathbb {E}} [ \underset {P \in \mathbf {P} ^ {+}} {\mathbb {E}} [ f _ {\gamma} (P, Y) ] - \underset {P \in \mathbf {P} ^ {-}} {\mathbb {E}} [ f _ {\gamma} (P, Y) ] ]
$$
As demonstrated in Figure 11, our semantic parser is comprised of three different parts, namely a resolution model, a breadth-first search model and a ranker model. The resolution model will try to figure out what are the entities appearing in the table and what are the numbers it needs to infer. These results are pushed to a buffer as the initial point, then the BFS search will try to compose plausible logical forms based on the values from the buffer. However, most of the synthesized logical forms are not relevant to the semantics the sentence is aimed to express. In the end, we need to train a ranker, which can learn to identify the most consistent logical form and use that to represent the formal semantics of given sentence.
D Qualitative Example
Next, we demonstrate some generated samples in Figure 12, which are generated from a table crawled from Wikipedia page<sup>3</sup>. Though most of the text generated by the model is coherent and reasonable, we do observe some disfluency like repetition, contradiction, erroneous sentences like the sentence 5. For the other sentences, three of them are logically correct, the first sentence contains quite complex logic with three different symbolic operations "argmax, argmin, after". The fourth and sixth sentences involve operations like "filter, count". In contrast, the second and third examples
3https://en.wikipedia.org/wiki/2007%E2%80%9308_Golden_State_Warriors_season
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player	country	year (s) won	total	to par
larry nelson	united states	1981 , 1987	152	+ 8
jack nicklaus	united states	1963 , 1971 , 1973 1975 , 1980	152	+ 8
lee trevino	united states	1974 , 1984	152	+ 8
hubert green	united states	1985	153	+ 9
lanny wadkins	united states	1977	155	+ 11
dave stockton	united states	1970 , 1976	157	+ 13
larry nelson , jack nicklaus , and lee trevino all shot 8 strokes over par  
larry nelson , lee trevino , and dave stockton each won twoPGA championships in the 1970s - 1980s  
jack nicklaus had more PGA championship wins than larry nelson and lee tevino combined  
dave stockton shot five strokes worse than larry nelson , jack nicklaus , and lee trevino  
three golfers shot worse than 8 strokes over par
Figure 9: Example from LOGICNLG.
round	date	opponent	venue	result	attendance
r3	8 january 2002	wycombe wanderers	a	2 - 2	9921
r3r	15 january 2002	wycombe wanderers	h	1 - 0	11894
r4	26 january 2002	york city	a	2 - 0	7563
r5	16 february 2002	walsall	a	2 - 1	8766
qf	10 march 2002	west bromwich albion	a	1 - 0	24811
sf	14 april 2002	chelsea	n	0 - 1	36147
the lowest attendance when fullham won was 7563
fullham fc only played one time at venue h
fullham fc played three times in the month of january
fullham fc faced the wycombe wanderers two times in the month of january
the only defeat of fullham for the 4 first months of 2002 fc was when they face chelsea
Figure 10: Example from LOGICNLG.
Figure 11: The BFS-based parser used in our evaluation.
are factually incorrect as the team only competes with "Seattle" once and the 3 games are not in a row. We can see that the errors are quite diversified, it is difficult to debug what is the source of these errors by simply looking into the deep generation model. In the future, more interpretable generation model need to be built to make the inference process more transparent.
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Title: Golden State Warrior: NBA Season 2007-2008
Date	Visitor	Score	Home	Attendance	Leading Player	Record
12 / 2	golden state warriors	109 - 96	seattle supersonics	11461	stephen jackson	9 - 7
12 / 3	orlando magic	117 - 123	golden state warriors	18527	stephen jackson	9 - 8
12 / 7	miami heat	120 - 113	golden state warriors	19596	stephen jackson	11 - 8
12 / 28	denver nuggets	120 - 124	golden state warriors	20001	stephen jackson	17 - 13
12 / 16	golden state warriors	87 - 109	detroit pistons	22076	matt barnes	13 - 11
12 / 17	golden state warriors	125 - 117	memphis grizzlies	10549	stephen jackson	14 - 11
1. The game with the lowest in Attendance took place after the game with the highest in Attendance.
$\times$  2. The Golden State Warrior played against the Seattle Supersonics 2 time.
$\times 3$  The Warrior won 3 game in a row during the 2007 - 08 Season.
√ 4. The Golden State Warrior lost 2 game when playing at Home.
$\times 5$  . There were 4 time that was a Leading Scorer, and 4 time that was a Leading Scorer.
$\checkmark$  6. Stephen Jackson was the leading scorer 5 different times during the 2007 - 08 Season.
Figure 12: The statements generated by GPT-TabGen model with random sampling.
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