### Table 1 shows 15 situations in which the mode interaction condition (IC) holds and gives the theorems which applies to this situation. In Table 1, %2; %3; %4 are certain irreducible representations of various H, not all of which we de ne precisely. For H = D1 3 (or D2 3), %3 denotes the two-dimensional irreducible representation. For H = K1 6(K2 6; K3 6) %3 and %4 denote two nontrivial one-dimensional irreducible representations.

1993

"... In PAGE 18: ...16: IC cannot be satis ed. O { IC does not hold Table1 : Mode Interaction condition for D6... ..."

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### Table 4: Performance of the overall best theorem prover on individual classes of the RTE dataset.

2005

"... In PAGE 6: ... We report the raw accuracy and the con dence weighted score (CWS) in Table 3.5 Table4 shows the performance of the theorem prover split by RTE example class (as illustrated... In PAGE 7: ...3%.) Interestingly, the performance varies heavily by class, (see Table4 ), possibly indicating that some classes are inherently more dif cult. The baseline accuracy is close to random guessing, and the difference between our system performance and the baseline performance on the test set is statistically signi - cant (p lt; 0:02).... In PAGE 7: ... Since our logical formu- lae essentially restate the information in the dependency graph, our abductive inference and learning algorithms are not tied to the logical representation; in particular, the inference algorithm can be modi ed to work with these graph-based representations, where it can be interpreted as a graph-matching procedure that prefers globally consis- tent matchings. Table4 shows that certain classes require more effort in linguistic modeling, and improvements in those classes can lead to great overall gains in performance. The current rep- resentation fails to capture some important interactions in its dependencies (e.... ..."

Cited by 14

### Table 4: Performance of the overall best theorem prover on individual classes of the RTE dataset.

2005

"... In PAGE 6: ... We report the raw accuracy and the confidence weighted score (CWS) in Table 3.5 Table4 shows the performance of the theorem prover split by RTE example class (as illustrated... In PAGE 7: ...3%.) Interestingly, the performance varies heavily by class, (see Table4 ), possibly indicating that some classes are inherently more difficult. The baseline accuracy is close to random guessing, and the difference between our system performance and the baseline performance on the test set is statistically signifi- cant (p lt; 0.... In PAGE 7: ... Since our logical formu- lae essentially restate the information in the dependency graph, our abductive inference and learning algorithms are not tied to the logical representation; in particular, the inference algorithm can be modified to work with these graph-based representations, where it can be interpreted as a graph-matching procedure that prefers globally consis- tent matchings. Table4 shows that certain classes require more effort in linguistic modeling, and improvements in those classes can lead to great overall gains in performance. The current rep- resentation fails to capture some important interactions in its dependencies (e.... ..."

Cited by 14

### Table 3. Composition Theorems

1999

"... In PAGE 7: ...2 Composition theorems In this section we discuss some useful theorems, that can be proved exploiting the semantics in Table 2 and the de nitions in the previous subsection. We distinguish liveness ( Table3 , 1{6) and safety (Table 3, 7{15). (1) Reliable Communication: this theorem characterizes remote writings, linking the su cient cause in the sender to the e ect in the recipient.... ..."

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### Table 4. Composition Theorems.

1999

"... In PAGE 7: ...4 Composition Theorems In this section we discuss some useful theorems, that can be proved exploiting the semantics in Table 3 and the de nitions in the previous subsection. We distinguish liveness ( Table4 , 4{8) and safety (Table 4, 9{15). Most theorems refer to the new operators, and only few of them refer to Unity operators: the former are those needed to prove the re nement templates presented in this paper.... ..."

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### Table 2. The number of theorems

2005

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### TABLE 1: THE COVERING FOR THEOREM ??

2002

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