### Table 5: Transforming an existential sentence to a singularity problem.

1999

"... In PAGE 15: ...roof. The proof is analogous to the proof of Lemma 9, but we handle negation di erently. To construct the matrix M, we modify the unquanti ed formula apos; using the rewriting rules of Table 7. Steps 3-5 in Table 7 correspond closely to steps 1-3 in Table5 , except that we have no rule for negation. The rst two steps of Table 7 serve to remove negation.... ..."

Cited by 7

### Table 5: Transforming an existential sentence to a singularity problem.

"... In PAGE 15: ...roof. The proof is analogous to the proof of Lemma 9, but we handle negation di erently. To construct the matrix M, we modify the unquanti ed formula apos; using the rewriting rules of Table 7. Steps 3-5 in Table 7 correspond closely to steps 1-3 in Table5 , except that we have no rule for negation. The rst two steps of Table 7 serve to remove negation.... ..."

### Table 5: Transforming an existential sentence to a singularity problem. F = GF (q) Rewrite rules

"... In PAGE 15: ...roof. The proof is analogous to the proof of Lemma 9, but we handle negation di erently. To construct the matrix M, we modify the unquanti ed formula apos; using the rewriting rules of Table 7. Steps 3-5 in Table 7 correspond closely to steps 1-3 in Table5 , except that we have no rule for negation. The rst two steps of Table 7 serve to remove negation.... ..."

### Table 5: Completion rules

### Table 3. Sound and complete system for local model checking from [7]

### Table 1. The number of pages (bodies of rules) with the certain length of rankings based on direct and complex rules; minimal confidence equals 1%

2004

"... In PAGE 12: ... 7. The number of partial indirect rules (left); the comparison of the number of direct, complete indirect and complex rules (right) discovered for different values of minimal support Up to 18% (818) pages may have a very short ranking list (less than 5 positions) derived from direct rules ( Table1 ) while this rate reaches only max. 0.... ..."

Cited by 4

### Table 1: Rules of the Antisequent Calculus

"... In PAGE 2: ... The rules for the antisequent calculus can be found in Table 1. The antisequent calculus in Table1 was shown to be sound and complete by Bonatti ((Bonatti 1993)), making use of the classical propositional Soundness and Completeness theorems. Skeptical Sequent Calculus for Autoepistemic Logic We will use the propositional fragment of LK and its antise- quent counterpart given in Table 1, extended to the propo- sitional language LL.... In PAGE 2: ... The antisequent calculus in Table 1 was shown to be sound and complete by Bonatti ((Bonatti 1993)), making use of the classical propositional Soundness and Completeness theorems. Skeptical Sequent Calculus for Autoepistemic Logic We will use the propositional fragment of LK and its antise- quent counterpart given in Table1 , extended to the propo- sitional language LL. In dealing with lack of proof, we will need not only to assert that such-and-such proposition is proved, but to state explicitly how it was proved.... ..."

### Table 1. Descriptions of Sound Renderings

"... In PAGE 4: ... Three different aural renderings related to this code are described in Table 1. We use English punctuation in Table1 as a mechanism to depict how the code would sound. For example, in the Block Composition column, the colon after the while condition indicates an expectant pause, rather than, say, the completion of a sentence.... ..."

### Table 5: Evaluation of Letter-To-Sound rules.

"... In PAGE 6: ... The evaluation pronunciations were cho- sen by selecting every 10th word in the alphabetically sorted pronunciation dictionary. The results of the letter-to-sound rules are shown in Table5 . The letter-to-sound rules man- aged to correctly predict 85.... ..."