SlowGuess/NeurIPS_2023_OCR huggingface dataset:
To address research question (RQ1), we propose a variant of ConE called ConE(temporal) that incorporates temporal information into the static query embedding. The only difference between ConE and ConE(temporal) is the projection operator used. In ConE(temporal), the projection operator incorporates temporal information through a technique called TTransE, which uses the temporal embedding of timestamps. In terms of formulation, the projection operator for ConE(temporal) is given by  $\mathcal{P}_e(\mathbf{V}_q,\mathbf{r},\mathbf{V}_t) = g(\mathbf{MLP}(\mathbf{V}_q + \mathbf{r} + \mathbf{V}_t))$ , while for ConE it is given by  $\mathcal{P}_e(\mathbf{V}_q,\mathbf{r},\mathbf{V}_t) = g(\mathbf{MLP}(\mathbf{V}_q + \mathbf{r}))$ . Note that  $\mathbf{V}_q,\mathbf{r},\mathbf{V}_t$  are cone embeddings.
From Table 17, we observe that there is slightly improvement in terms of MRR when comparing ConE(temporal) with ConE. It shows that the temporal information can help to improve the performance of static query embedding on answering entities over TKGs. However, the improvement is not significant, which indicates that simply aware of the temporal information is not enough to promote the static query embedding to efficient temporal one.
Next, we wonder if it could help when we utilize more queries involving time logic, which provides more temporal information. Therefore, we address research question (RQ2) by proposing a variant of ConE and TFLEX, called X(ConE), that enhances the static query embedding with temporal logic. X(ConE) replaces the entity part of temporal feature-logic embedding with ConE, as is introduced in Section 5.2. In the other view, X(ConE) is based on ConE, using cone embedding concatenated with the time part of temporal feature-logic embedding, which can handle temporal logic.
From Table 17, to our surprise,  $\mathbf{X}(\mathbf{ConE})$  performs worse than ConE and TFLEX. The concatenation of cone embedding and feature-logic embedding does not help to improve the overall performance of temporal complex reasoning. This is because cone embedding is geometric, while temporal feature-logic embedding is fuzzy. We think there is a mismatch or semantic conflict between the two embeddings, which leads to the poor performance of  $\mathbf{X}(\mathbf{ConE})$ .
Be aware that we do not deny the importance of temporal logic. In fact, temporal logic is very important for temporal complex reasoning (See Ablation on time part in Section 5.2). However, we think that it is not a good idea to promote the static query embedding to temporal one by simply concatenating the geometric embedding with the fuzzy embedding. The right way to promote remains an open question.
Table 17: Average MRR results for TFLEX and the variants of ConE.  $\mathbf{AVG}_e$  denotes average of  $\mathrm{avg}_e$ ,  $\mathrm{avg}_{e,\mathcal{C}_e}$  and  $\mathrm{avg}_{\mathcal{U}_e}$ .  $\mathbf{AVG}$  denotes average of all groups.
Dataset	Model	avge	avgε,Ce	avgUe	avgt	avgt,Ct	avgUt	avgx	AVGe	AVG
ICEWS14	ConE	41.94	44.88	26.47	37.76
ConE(temporal)	42.23	44.94	27.63	38.27
X(ConE)	40.93	42.15	25.46	16.41	35.24	24.07	26.65	36.18	30.13
TFLEX	56.79	50.82	35.74	17.56	36.37	26.24	28.03	47.78	35.93
ICEWS05-15	ConE	40.93	43.52	43.02	42.49
ConE(temporal)	40.74	43.34	43.14	42.41
X(ConE)	36.29	38.12	36.37	4.41	29.49	26.40	21.69	36.93	27.54
TFLEX	48.99	46.17	54.37	4.39	30.16	28.69	24.26	49.84	33.72
GDELT-500	ConE	18.44	12.67	6.96	12.69
ConE(temporal)	18.51	12.67	7.30	12.83
X(ConE)	17.83	12.34	7.41	3.16	3.93	6.35	6.17	12.53	8.17
TFLEX	19.60	13.52	7.58	5.38	6.31	6.71	6.17	13.57	9.32
D Visualization of Semantic Changes by Neural Temporal Operators
In this section, we present more visualization of the semantic changes of temporal operators in TFLEX. The examples are randomly selected in the test set of ICEWS14. The visualization is shown in Figure 10, Figure 11 and Figure 12. We attach the anchors and the ground-truth answers in the corresponding caption of figures. From the figures, we observe that the model correctly ranks the hard answers at top when answering query Pt. It can also be seen from the figure that the semantic changes of temporal operators aPt and bPt are intuitive and reasonable.
Figure 10: Score distributions of Pt, bPt and aPt, where  $s$  is Citizen (India),  $r$  is Criticize or denounce,  $o$  is Sadhu (India), ground-truth answer of Pt is 2014-03-27.
Figure 11: Score distributions of Pt, bPt and aPt, where  $s$  is Citizen (India),  $r$  is Use unconventional violence,  $o$  is Chief Secretary Chandra, ground-truth answer of Pt is 2014-05-11.
Figure 12: Score distributions of Pt, bPt and aPt, where  $s$  is Mohammad Javad Zarif,  $r$  is Appeal for economic cooperation,  $o$  is United Arab Emirates, ground-truth answer of Pt is 2014-04-14.
E Explaining Answers with Temporal Feature-Logic Framework
In this section, we present the explanation of answers given by TFLEX. Below we take the query "e2i" as an example. The temporal query "e2i" is defined as follows:  $q[V_{?}] = V_{?}, \exists V_{a}, V_{b}, r_{1}(e_{1}, V_{a}, t_{1}) \land r_{2}(e_{2}, V_{b}, t_{2})$ . Let's consider the specific query: "Who was consulted by Mohammad Javad Zarif on 2014-04-07 and consulted Mohammad Javad Zarif on 2014-04-07?" In this example,  $e_{1} =$  "Mohammad Javad Zarif",  $r_{1} =$  "consulted by",  $t_{1} =$  "2014-04-07",  $r_{2} =$  "consulted", and  $t_{2} =$  "2014-04-07". We use TFLEX to execute the query and obtain the answers. The answers are categorized into easy, hard, and wrong ones. Table 18 presents the five most likely answers and their rankings for interpretation. From the table, we observe that TFLEX ranks the answers "Mohammad Javad Zarif", "Sebastian Kurz", "China" and "Catherine Ashton" high, while ranking the wrong answer "Iran" low. TFLEX even infers a hard answer "Catherine Ashton" with higher score than two easy answers "Sebastian Kurz" and "China". This demonstrates that TFLEX successfully identifies the correct answers using complex reasoning and distinguishes them from the wrong ones.
Navigation: Pt(13), Pe(14), Pe2(15), Pe3(16), Pe_Pt(17), e2i(18), e3i(19), e2i_Pe(20), Pe_e2i(21), Pe_t2i(22), t2i(23), t3i(24), t2i_Pe(25), Pt_se2i(26), Pt_oe2i(27), t2i_NPt(28), t2i_PtN(29), Pe_t2i_PtPe_NPt(30), e2i_NPe(31), e2i_PeN(32), Pe_e2i_Pe_NPe(33), e2i_N(34), e3i_N(35), e2u(36), Pe_e2u(37), Pt_sPe(38), Pt_oPe(39), t2i_N(40), t3i_N(41), t2u(42), Pe_t2u(43), Pe_aPt(44), Pe_bPt(45), Pe_at2i(46), Pe bt2i(47), between(48).
Figure 13: Intermediate variable assignments and ranks for example Pt query. Correctness indicates whether the answer belongs to the ground-truth set of answers.
Figure 14: Intermediate variable assignments and ranks for example Pe query. Correctness indicates whether the answer belongs to the ground-truth set of answers.
Figure 15: Intermediate variable assignments and ranks for example Pe2 query. Correctness indicates whether the answer belongs to the ground-truth set of answers.
Figure 16: Intermediate variable assignments and ranks for example Pe3 query. Correctness indicates whether the answer belongs to the ground-truth set of answers.
Query Sentence	Who was criticized or denounced on 2014-08-26 by the person who made a statement on 2014-02-05 at the place where the presidential movement made an appeal or request on 2014-04-24?
Temporal Query	q[V?] = V?, ∃Va, Vb, r1(e1, Va, t1) ∧ r2(Va, Vb, t2) ∧ r3(Vb, V?, t3)
Rank	Query Answers	Correctness	Answer Type
1	Government (France)	✔	Easy
2	France	×	-
3	François Hollande	✔	Hard
4	Angela Merkel	×	-
5	Citizen (International)	×	-
Pe_Pt Pe(e1,r1, before(Pt(e2,r2,e3)))
$e_1$  : Citizen (Thailand)
$r_1$  : Arrest, detain, or charge with legal action
$e_2$  : Police (Greece)
$r_2$  : Arrest, detain, or charge with legal action
$e_3$  : Illegal Immigrant (Greece)
Query Sentence	Who arrested, detained, or charged the citizen (Thailand) with legal action after Police (Greece) arrested, detained, or charged the illegal immigrant (Greece) with legal action?
Temporal Query	q[V?] = V2, ΝTa, r1(e1, V2, Ta) ∧ r2(e2, e3, Ta)
Rank	Query Answers	Correctness	Answer Type
1	Military (Thailand)	✓	Easy
2	Municipal Court (Thailand)	✓	Easy
3	Thailand	✓	Hard
4	National Council for Peace and Order of Thailand	X	-
5	Police (Cambodia)	X	-
Figure 17: Intermediate variable assignments and ranks for example Pe_Pt query. Correctness indicates whether the answer belongs to the ground-truth set of answers.
$e_1$  : Mohammad Javad Zarif
$r_1$  : Consult
$t_1$  : 2014-04-07
$\varepsilon_{2}$  : Mohammad Jayad Zarif
T
to: 2014-04-07
Query Sentence	Who was consulted by Mohammad Javad Zarif on 2014-04-07 and consulted Mohammad Javad Zarif on 2014-04-07?
Temporal Query	q[V?] = V?, r1(e1, V?, t1) ∧ r2(e2, V?, t2))
Rank	Query Answers	Correctness	Answer Type
1	Mohammad Javad Zarif	✔	Easy
2	Catherine Ashton	✔	Hard
3	Sebastian Kurz	✔	Easy
4	China	✔	Easy
5	Iran	✘	-
Figure 18: Intermediate variable assignments and ranks for example e2i query. Correctness indicates whether the answer belongs to the ground-truth set of answers.
e3i And3(Pe(e1, r1, t1), Pe(e2, r2, t2), Pe(e3, r3, t3))
$e_1$  : Joseph Robinette Biden
$r_1$  : Discuss by telephone
$t_1$  ： 2014-10-05
$e_2$  : Joseph Robinette Biden
$r_2$  : Discuss by telephone
$t_2$  : 2014-10-05
$e_3$  : Saud bin Faisal bin Abdul-Aziz
$r_3$  : Make a visit
$t_8$  : 2014-01-20
Figure 19: Intermediate variable assignments and ranks for example e3i query. Correctness indicates whether the answer belongs to the ground-truth set of answers.
Query Sentence	Where was Joseph Robinette Biden discussed by telephone on 2014-10-05 and visited by Saud bin Faisal bin Abdul-Aziz on 2014-01-20?
Temporal Query	q[V?] = V?, r1(e1, V?, t1) ∧ r2(e2, V?, t2) ∧ r3(e3, V?, t3)
Rank	Query Answers	Correctness	Answer Type
1	UAE Armed Forces	✔	Easy
2	United Arab Emirates	✔	Hard
3	Middle East	×	-
4	Morocco	×	-
5	Abdel Fattah Al-Sisi	×	-
Figure 20: Intermediate variable assignments and ranks for example e2i_Pe query. Correctness indicates whether the answer belongs to the ground-truth set of answers.
Query Sentence	Where was occupied territory on 2014-03-01 and was visited on 2014-06-04 by the person who Obaid Humaid Al Tayer made a statement on 2014-06-11?
Temporal Query	q[V?] = V?, ∃Va, r1(e1, Va, t1) ∧ r2(Va, V?, t2) ∧ r3(e2, V?, t3)
Rank	Query Answers	Correctness	Answer Type
1	Iran	✔	Easy
2	China	×	-
3	Iraq	×	-
4	France	×	-
5	Afghanistan	×	-
Figure 21: Intermediate variable assignments and ranks for example Pe_e2i query. Correctness indicates whether the answer belongs to the ground-truth set of answers.
Query Sentence	Where was consulted on 2014-03-25 by the place where Labor Union (Croatia) made an appeal or request on 2014-02-03 and was consulted by Government (Croatia) on 2014-03-25?
Temporal Query	q[V?] = V?, ∃Va, r1(e1, Va, t1) ∧ r2(e2, Va, t2) ∧ r3(Va, V?, T3)
Rank	Query Answers	Correctness	Answer Type
1	Labor Union (Croatia)	✔	Hard
2	Business (Croatia)	✘	-
3	Government (Croatia)	✔	Easy
4	Ministry (Croatia)	✔	Easy
5	Branko Grcic	✘	-
Figure 22: Intermediate variable assignments and ranks for example Pe_t2i query. Correctness indicates whether the answer belongs to the ground-truth set of answers.
Query Sentence	Who signed a formal agreement with Government (South Africa) at the time when Gazprom signed a formal agreement with China and Mzukisi Fatyela made a statement to Police (South Africa)?
Temporal Query	q[V?] = V?, ∃Ta, r1(e1, V?, Ta) ∧ r2(e2, e3, Ta) ∧ r3(e5, e5, Ta)
Rank	Query Answers	Correctness	Answer Type
1	South Africa	✔	Easy
2	Tom Motsoahae Thabane	✘	-
3	China	✘	-
4	Bank (China)	✘	-
5	Henry Rotich	✘	-
Figure 23: Intermediate variable assignments and ranks for example t2i query. Correctness indicates whether the answer belongs to the ground-truth set of answers.
Query Sentence	At what time did Barack Obama negotiate with and consult Xi Jinping?
Temporal Query	q[T?] = T?, r1(e1, e2, T?) ∧ r2(e3, e4, T?)
Rank	Query Answers	Correctness	Answer Type
1	2014-11-15	✓	Easy
2	2014-03-24	✓	Easy
3	2014-11-12	✓	Easy
4	2014-11-11	✓	Easy
d 5	2014-11-14	✓	Easy
Figure 24: Intermediate variable assignments and ranks for example t3i query. Correctness indicates whether the answer belongs to the ground-truth set of answers.
Figure 25: Intermediate variable assignments and ranks for example t2i_Pe query. Correctness indicates whether the answer belongs to the ground-truth set of answers.
Figure 26: Intermediate variable assignments and ranks for example Pt_se2i query. Correctness indicates whether the answer belongs to the ground-truth set of answers.
Figure 27: Intermediate variable assignments and ranks for example Pt_oe2i query. Correctness indicates whether the answer belongs to the ground-truth set of answers.
Query Sentence	When did Japan engage in diplomatic cooperation with South Korea, Mohammad Javad Zarif make a statement to Iran, and François Hollande make a statement to France?
Temporal Query	q[T?] = T?, r1(e1, e2, T?) ∧ r2(e3, e4, T?) ∧ r1(e5, e6, T?)
Rank	Query Answers	Correctness	Answer Type
1	2014-09-18	✔	Hard
2	2014-09-20	✔	Easy
3	2014-08-22	✔	Easy
4	2014-07-01	✔	Hard
5	2014-08-16	✘	-
Query Sentence	When did Activist (Somalia) fight with small arms and light
weapons with Armed Gang (Somalia) while
Citizen (Oman) en-gage in a symbolic act with the
person with whom finance /
Economy / Commerce / Trade Ministry (Oman) shared intelli-gence or information on 2014-01-06?
Temporal Query	q[T?] = T?, ∃Va, r1(e1, Va, t1) ∧ r2(Va, e2, T?) ∧ r3(e3, e4, T?)
Rank	Query Answers	Correctness	Answer Type
e1: Finance / Economy / Commerce / Trade Ministry (Oman)
r1: Share intelligence or information	1	2014-01-30	✔ Easy
t1: 2014-01-06	2	2014-02-05	✘ -
r2: Engage in symbolic act-1	3	2014-01-29	✘ -
e2: Citizen (Oman)	4	2014-02-07	✘ -
e3: Activist (Somalia)	5	2014-02-04	✘ -
r3: fight with small arms and light
weapons-1	5	2014-02-04	✘ -
e4: Armed Gang (Somalia)	5	2014-02-04	✘ -
Pt_le2i Pt(e2i(c1, r1, t1, e2, r2, t2), r3, c3)
e1: r1: r2: e3:	And	Temporal Query	q[T?] = T?, ∃Va, r1(e1, Va, t1) ∧ r2(e2, Va, t2) ∧ r3(Va, e3, T?)
Rank	Query Answers	Correctness	Answer Type
e1:	Iran
r1:	Make a visit-1
t1:	2014-03-09
e2:	Iran
r2:	Host a visit
t2:	2014-03-09
r3:	Engage in negotiation
e3:	Iran
5	2014-03-09	√	Easy
Easy
Easy
Easy
Easy
Easy
Query Sentence	When did Armenia cooperate militarily with the country that cooperates militarily with Armenia on 2014-12-08 and 2014-07-02?
Temporal Query	q[V2] = V?, ∃Va, r1(e1, Va, T?) ∧ r2(e2, Va, t1) ∧ r3(e3, Va, t2)
Rank	Query Answers	Correctness	Answer Type
1	2014-12-08	✔	Easy
2	2014-07-02	✔	Easy
3	2014-05-06	✔	Easy
4	2014-10-26	✔	Easy
5	2014-07-17	✘	-
21_NPTimeAnd(TimeNot  $(\text{P} (Pe(e_1,r_1,t_1),r_2,e_2))$ $P(t_{e3},r_{3},e_{4}))$
e1: Edgum Rankevics  
 $\mathbf{r}_1$  : Express intent to meet or negotiate  
 $\mathbf{f}_1$  : 2014-04-22  
 $\mathbf{r}_2$  : Consult  
 $\mathbf{e}_2$  : Catherine Ashton  
 $\mathbf{e}_3$  : Japan  
 $\mathbf{e}_4$  : Express intent to meet or negotiate  
 $\mathbf{e}_5$  : Barack Obama
Query Sentence	When did Barack Obama express intent to meet or negotiate with Japan, and on that day, Catherine Ashton wasn’t consulted by the person Edgars Rinkevics expressed intent to meet or negotiate with on 2014-04-22?
Temporal Query	q[T?] = T?, ∃Va, r1(e1, Va, t1) ∧ ¬r2(Va, e2, T?) ∧ r3(e3, e4, T?)
Rank	Query Answers	Correctness	Answer Type
1	2014-04-17	✔	Easy
2	2014-04-18	✔	Easy
3	2014-02-13	✔	Easy
4	2014-04-05	✔	Easy
5	2014-02-11	✘	-
t2iPTn TimeAnd  $\mathrm{Pt}(Pe(e_1,r_1,t_1),r_2,e_2)$  ,TimeNot  $\mathrm{Pt}(e_3,r_3,e_4))$
Figure 28: Intermediate variable assignments and ranks for example t2i_NPt query. Correctness indicates whether the answer belongs to the ground-truth set of answers.
Query Sentence	When was the citizen (Greece) made an appeal or request by the country that made an appeal or request to the Party President (Greece), and on that day, Angela Merkel did not express intent to meet or negotiate with Evo Morales?
Temporal Query	q[T?] = T?, ∃Va, r1(e1, Va, t1) ∧ r2(Va, e2, T?) ∧ ¬r3(e3, e4, T?)
Rank	Query Answers	Correctness	Answer Type
1	2014-05-16	✓	Easy
2	2014-07-24	✓	Easy
3	2014-05-25	✓	Easy
4	2014-04-29	✓	Easy
5	2014-07-29	✓	Easy
Figure 29: Intermediate variable assignments and ranks for example t2i_PtN query. Correctness indicates whether the answer belongs to the ground-truth set of answers.
Query Sentence	Who discussed by telephone with Sergey Viktorovich Lavrov on the day when Hun Sen was threatened by the person who was arrested, detained, or charged with legal action by the Buddhist (Cambodia) on 2014-04-30, and on that day, Education (Colom-bia) made a statement to Eric Garner?
Temporal Query	q[V2] = V2; ∃Va, Ta, r1(e1, V2, Ta) ∧ r2(e2, Va, t1) ∧ r3(Va, e3, Ta) ∧ ¬r4(e4, e5, Ta)
Rank	Query Answers	Correctness	Answer Type
1	John Kerry	✓	Hard
2	Cabinet / Council of Ministers / Advisors (United States)	✓	Easy
3	Catherine Ashton	✗	-
4	Sergey Viktorovich Lavrov	✗	-
5	Joseph Robinette Biden	✗	-
Figure 30: Intermediate variable assignments and ranks for example Pe_t2i_N query. Correctness indicates whether the answer belongs to the ground-truth set of answers.
Figure 31: Intermediate variable assignments and ranks for example e2i_NPe query. Correctness indicates whether the answer belongs to the ground-truth set of answers.
Query Sentence	Who visited Iran on 2014-04-29 and did not make a statement at the place where Carlos Saul Menem made a statement on 2014-09-20?
Temporal Query	q[V?] = V?, ∃Va, Vb, r1(e1, Va, t1) ∧ ¬r2(Va, Vb, t2) ∧ r3(e2, V?, t3)
Rank	Query Answers	Correctness	Answer Type
1	Santos Edelmar Lopez	✔	Easy
2	Simon Gass	✔	Easy
3	Sebastian Kurz	✔	Easy
4	Catherine Ashton	✘	-
5	Iran	✘	-
e2i_PeN And(Pe(Pe(e1, r1, t1), r2, t2), Not(Pe(e2, r3, t3)))
Figure 32: Intermediate variable assignments and ranks for example e2i_PeN query. Correctness indicates whether the answer belongs to the ground-truth set of answers.
$\epsilon_{1}$  : Energy Department/Ministry (Turkey)
$r_1$  : Express accord
$t_1$  ： 2014-03-27
r2: Make pessimistic c 1014.03.17
t2: 2014-03-15Ta: Mainland Affinity
C2: Mainland Affairs 1: Make a visit
$r_3$  : Make a visit  $t_0$  : 2014-02-11
Query Sentence	Who was commented pessimistically on 2014-03-13 by the person who expressed accord to Energy Department/Ministry (Turkey) on 2014-03-27 and not visited by Mainland Affairs Council on 2014-02-11?
Temporal Query	q[V?] = r3(e2,V?,t3)	V?, ∃Va, Vb, r1(e1, Va, t1) ∧ r2(Va, V?, Tb) ∧ /
Rank	Query Answers	Correctness	Answer Type
1	Member of the Judiciary (Turkey)	✔	Easy
2	Lawyer/Attorney (Turkey)	✔	Hard
3	Justice and Development Party	✕	-
4	Other Authorities / Officials (Turkey)	✕	-
5	Party Member (Turkey)	✕	-
Pe_e2i_Pe_NPe Pe(And(Pe(e1, r1, t1), Not(Pe(e2, r2, t2))), r3, t3)
Figure 33: Intermediate variable assignments and ranks for example Pe_e2i_N query. Correctness indicates whether the answer belongs to the ground-truth set of answers.
Treasury/Finance Ministry (Eritrea)
e2: Drug Gang (Beltrán-Leyva Cartel)
r2:Arrest,detain,or charge with legal action 140120141016
12. 2014-16-18 r:1 Energe in neoation
fao 2014:10:21
Query Sentence	On 2014-10-21, who negotiated with the person who consulted with the Treasury/Finance Ministry (Eritrea) on 2014-09-17 but did not arrest, detain, or charge Drug Gang (Beltrán -Leyva Cartel) with legal action on 2014-10-16?
Temporal Query	q[V?] = V?, ∃Va, Vb, r1(e1, Va, t1) ∧ / r2(e2, Va, t2) ∧
r3(Va, V?, t3)
Rank	Query Answers	Correctness	Answer Type
1	South Korea	✔	Easy
2	Japan	×	-
3	China	✔	Hard
4	North Korea	×	-
5	Thailand	×	-
e2i_N And  $(Pe(e_1,r_1,t_1),Not(Pe(e_2,r_2,t_2)))$
Figure 34: Intermediate variable assignments and ranks for example e2i_N query. Correctness indicates whether the answer belongs to the ground-truth set of answers.
$e_1$  ：
1: Bally composition againsst-1
102014-03-11
6.1. Citizen (Brunei)
c2. . CunZi (Blunt) 1.4 Make amputathic comment
$r_2$  : makeepsilonof  
 $\mathbf{t}:$  2014-03-26
Query Sentence	Who rallied opposition against Botswana on 2014-03-11 but was not empathetically commented upon by Citizen (Brunei) on 2014-03-26?
Temporal Query  $q[V_{?}] = V_{?},r_{1}(e_{1},V_{?},t_{1})\wedge \neg r_{2}(e_{2},V_{?},t_{2})$
Rank	Query Answers	Correctness	Answer Type
1	Industry (Botswana)	✔	Easy
2	Citizen (Botswana)	✔	Hard
3	Richard Sezibera	✘	-
4	Labor and Employment Ministry (Botswana)	✘	-
5	Paul Kagame	✘	-
e3i_N And3(Pe(e1, r1, t1), Pe(e2, r2, t2), Not(Pe(e3, r3, t3)))
Figure 35: Intermediate variable assignments and ranks for example e3i_N query. Correctness indicates whether the answer belongs to the ground-truth set of answers.
$e_1$  : Envoy (Kazakhstan)
$r_1$  : Praise or endorse
t1: 2014-05-19
$e_2$  ： RIA Novosti
Sign formal agreement
t2: 2014-12-12
Gc:Goverpor (South Korea)
r1:Signformalagreement-1
1-Signif. for madagc
Query Sentence	Who was praised or endorsed by Envoy (Kazakhstan) on 2014-05-19 and signed a formal agreement with RIA Novosti on 2014-12-12 but not signed a formal agreement with Governor (South Korea) on 2014-05-09?
Temporal Query  $q[V_{7}] = V_{7},r_{1}(e_{1},V_{7},t_{1})\wedge r_{2}(e_{2},V_{7},t_{2})\wedge f_{3}(e_{3},V_{7},t_{3})$
Rank	Query Answers	Correctness	Answer Type
1	Iran	✔	Easy
2	Iraq	✕	-
3	China	✕	-
4	Afghanistan	✕	-
5	North Atlantic Treaty Organization	✕	-
Figure 36: Intermediate variable assignments and ranks for example e2u query. Correctness indicates whether the answer belongs to the ground-truth set of answers.
Figure 37: Intermediate variable assignments and ranks for example Pe_e2u query. Correctness indicates whether the answer belongs to the ground-truth set of answers.
Figure 38: Intermediate variable assignments and ranks for example Pt_sPe query. Correctness indicates whether the answer belongs to the ground-truth set of answers.
Figure 39: Intermediate variable assignments and ranks for example Pt_oPe query. Correctness indicates whether the answer belongs to the ground-truth set of answers.
Figure 40: Intermediate variable assignments and ranks for example t2i_N query. Correctness indicates whether the answer belongs to the ground-truth set of answers.
Query Sentence	When did Abu Bakr Abdullah al-Qirbi discuss with Mohammad Javad Zarif by telephone, and on that day Senate (Slovakia) did not reject Justice Department/Ministry (Slovakia)?
Temporal Query	q[T?] = T?, r1(e1, e2, T?) ∧ ¬r2(e3, e4, T?)
Rank	Query Answers	Correctness	Answer Type
1	2014-01-19	✔	Easy
2	2014-01-18	✔	Hard
3	2014-11-02	X	-
4	2014-02-02	X	-
5	2014-12-13	X	-
Figure 41: Intermediate variable assignments and ranks for example t3i_N query. Correctness indicates whether the answer belongs to the ground-truth set of answers.
Query Sentence	When did the Police (Egypt) use tactics of violent repression against protesters (Egypt) and the Police (Ukraine) use tactics of violent repression against protesters (Egypt), and on that day Information / Communication / Transparency Ministry (China) did not consult Warren Truss?
Temporal Query	q[T?] = T?, r1(e1, e2, T?) ∧ r2(e3, e4, T?) ∧ ¬r3(e5, e6, T?)
Rank	Query Answers	Correctness	Answer Type
1	2014-01-21	✔	Easy
2	2014-01-13	X	-
3	2014-01-22	X	-
4	2014-02-20	X	-
5	2014-01-14	X	Hard
Figure 42: Intermediate variable assignments and ranks for example t2u query. Correctness indicates whether the answer belongs to the ground-truth set of answers.
Query Sentence	When did citizens (Botswana) obstruct passage and block Nonofo Molefi or Zheng Zeguang make statements about China?
Temporal Query	q[T?] = T?, r1(e1, e2, T?) ∨ r2(e3, e4, T?)
Rank	Query Answers	Correctness	Answer Type
1	2014-04-09	✔	Easy
2	2014-05-21	✔	Easy
3	2014-05-20	✔	Hard
4	2014-05-22	X	-
5	2014-05-22	X	-
Figure 43: Intermediate variable assignments and ranks for example Pe_t2u query. Correctness indicates whether the answer belongs to the ground-truth set of answers.
Query Sentence	Who was appealed or requested by Citizen (Nigeria) on the day when the University of Cape Town consulted News Editor (Nigeria) or State Security Court (United Arab Emirates) arrested, detained, or charged Muslim (United Arab Emirates) with legal action?
Temporal Query	q[V?] = V?, ∃Ta, r1(e1, V?, Ta) ∧ (r2(e2, e3, Ta) ∨ r3(e4, e5, Ta))
Rank	Query Answers	Correctness	Answer Type
1	Government (Nigeria)	✔	Easy
2	Assemblies (Nigeria)	✔	Hard
3	Other Authorities / Officials (Nigeria)	✘	-
4	Head of Government (Nigeria)	✘	-
5	Citizen (Nigeria)	✘	-
Pe_aPt Pe(e1, r1, after(Pt(e2, r2, e3)))