### Table 3. Update postulates rewritten as modal logic rules

1997

"... In PAGE 9: ... One could consider stronger or weaker logics, according to applications. Some of the rules in Table3 , namely U4.1, U4.... In PAGE 9: ... As usual within the framework of modal logic, we can study the `correspondence properties apos; on R imposed by an axiom or rule. Theorem 6 A rule in Table3 holds in a frame F = hW; Ri i R has the corresponding property stated in Table 4.... In PAGE 22: ... x 3A(B_C) i 9y RjAj(x; y); y B_C i 9y1 RjAj(x; y1); y1 B or 9y2 RjAj(x; y2); y2 C i x 3AB _ 3AC. Theorem 6 A rule in Table3 holds in a frame F = hW; Ri i R has the corresponding property stated in Table 4. Proof.... ..."

Cited by 12

### Table III. Update postulates rewritten as modal logic rules

1997

Cited by 12

### Table 1. Katsuno/Mendelzon update postulates rewritten as modal logic axioms and rules

1997

"... In PAGE 2: ... As usual within the framework of modal logic, we can study the `correspondence properties apos; on R imposed by each of the postulates U1-U8. Theorem 5 (1) A postulate in Table1 holds in a frame F = hW;Ri i R has the corresponding property stated in Table 2. (2) The postulates U4.... ..."

Cited by 3

### TABLE 1 Some Typical Formal Rules of Inference Postulated as Part of Mental Logic by Many Psychologists

1998

Cited by 4

### Table 2 shows the logical links between the three sets of postulates, discarding classical abduction. The postulates entering in their definition are presented in bold characters. The derivation of other postulates is proved in the appendix.

### Table 2: Update postulates of Table 1 rewritten as modal logic axioms and rules

"... In PAGE 6: ...o. This occupies us for the remainder of this section. Theorem 3.2 An axiom scheme or rule in Table2 holds in a frame F = hW; Ri i R has the corresponding property stated in Table 3. Compare correspondence theorems for standard modal logic, eg.... ..."

### Table 3. Interpretation of Postulates (N1){(N4), (P1), (P2), and (P4).

2002

"... In PAGE 21: ...The interpretation of postulates (N1){(N4) in terms of update sequences is given in Table3 . The results show that (N1) and (N2) hold, whereas (N3) and (N4) fail.... In PAGE 21: ... Hence, in some sense, updates do not represent a loss in properties with respect to standard answer set semantics. Table3 contains also the interpretation of postulates (P1){(P6). As a matter of fact, since (P3) and (P6) coincide with (N1) and (N3), respectively, and (P5) admits no interpretation in terms of logic programs, only postulates (P1), (P2), and (P4) are included in Table 3.... In PAGE 21: ... Table 3 contains also the interpretation of postulates (P1){(P6). As a matter of fact, since (P3) and (P6) coincide with (N1) and (N3), respectively, and (P5) admits no interpretation in terms of logic programs, only postulates (P1), (P2), and (P4) are included in Table3 . Like the failure of (K6) and (U4), the failure of postulate (P1) showcases the syntax-dependency of update programs, as equivalent programs do not behave the same way under identical update information.... ..."

Cited by 38

### Table 1. Interpretation of Postulates (K1){(K8) and (U1){(U6).

2002

"... In PAGE 16: ... We thus do not consider the postulates involving the operator _. Given these considerations, Table1 summarizes our interpretation of postulates (K1){(K8) and (U1){(U6), and includes references whether the respective prop- erty holds or fails. We assume that P; P0 are sequences of ELPs, and P; P 0 denote single ELPs.... In PAGE 16: ...3, and can be easily adapted for dynamic logic programming too. As can be seen from Table1... ..."

Cited by 38

### Table 1. Formal verification using BAN logic.

"... In PAGE 9: ... The deduction is quite lengthy and we omit it. We only show the idealized protocol and stepwise results in Table1 and omit the detailed discussion of the process. Step 1 is trivial.... In PAGE 9: ... Since that member has the control over the generation of the Bloom filter, P believes the Bloom filter (Postulate (3)). Based on these postulates, we can mechanically deduct and get the results as shown in Table1 . Moreover, the logic forces us to explicitly write down our assumptions to clarify our design goals.... ..."