### Table 1: Expected size of recovered relation (jrj = 10; n = 12; p = 4; j j = 2) There are, as yet, no completely general results concerning the expected value of jr j in the overlapping case: the situation is apparently very complex and depends on the exact structure of . However, the following Proposition provides a useful formula for calculating this expected value: Proposition 6.1

"... In PAGE 17: ... For each constraint there are j jp possible values, so if r may be approximated by a random selection of tuples, we may use elementary probability arguments to show that: P (w[Sj] 2 Sj(r)) = 1 ? (1 ? 1=j jp)jrj Assuming, for the moment, that the constraints all act independently, we obtain the following expression for the expected size of the recovered relation, E(jr j) (see [20]): E(jr j) = j jn(1 ? (1 ? 1=j jp)jrj)q (2) This expression may be a useful approximation when the Si do not overlap, but, is much too optimistic for the cases we are interested in, which have a high degree of overlap. Table1 compares the values obtained from Equation 2 with the results of simulations for various values of q. It can be seen that the predicted values are much too small for larger values of q.... ..."

### Table 2. A proof system for propositional logic. (Ins1) cq ; = ;

"... In PAGE 8: ... As usual, we write _ for : ! , ^ for :(: _: ), and $ for ( ! )^( ! ). In Table2 we give a complete proof system for propositional logic. The signal insertion operation cq assigns propositional formulae to the states contained in frames.... In PAGE 8: ...2) and the axioms given in Table 3. Additionally, we can use identities = i $ is provable from the axiom schemas and the inference rule given in Table2 . The axioms in Table 3 express that signal insertion to a frame is tantamount to signal insertion to all its states, taken as frames (axioms (Ins1), (Ins5), (Ins6) and (TIns1)).... ..."

### Table 1. Formulas and their intended meaning

"... In PAGE 12: ... Additional aspects appearing on the stage in specific cases may be addressed by refining the system and adding new axioms. Table1 gives a number of modal formulas appearing in this paper, together with their intended meanings. The symbol a15 denotes a proposition, but all these formulas also appear with respect to an action a24.... ..."

### Table 1: Formulas and their intended meaning

"... In PAGE 7: ... The transition from proposition to action is achieved by a process of means-end-analysis. Table1 gives the formulas appearing in this paper, together with their intended meanings. The symbol apos; denotes a proposition and #0B an action.... ..."

### Table 1: Complexity results for positive propositional DDBs (i.e. without integrity clauses and negation) Semantics Inference of literal Inference of formula 9 model

1993

Cited by 31

### Table 1. Propositional Tableaux Rules rules

"... In PAGE 1: ... Let F be the set of L( )-formulas. Semantical de nitions for disjunction and negation in the Strong Kleene Logic are given in Table1 . Let true, false and unde ned be truth-values denoted with t; f and u.... In PAGE 3: ... 4 Automatization of Belief Change Using Tableaux 4.1 Classical Propositional Tableaux Propositional tableaux rules for non-atomic formulas, namely ; ( Table1 ) and negative rules are given now. rules cor- responds to conditions that must be satis ed symultaniously for twice subformulas.... ..."

### Table 1 summarizes the performance of the value-passing model checker and the propositional model checker on the property shown in Figure 5. The mea- surements were taken on a 600MHz Pentium III with 256MB running Linux 2.2. We checked the validity of that property for di erent values of domain size (n in that gure) on a speci cation of a two-link alternating bit protocol (ABP). The two-link version of the protocol is obtained by cascading two ABP speci cations, connecting the receiver process of one link to the sender of the next. We chose the two-link version since the single-link ABP is too small for any meaningful performance measurement. The space and time performance from the table shows that the value-passing model checker performs as well as the propositional one; the di erence in speeds can be attributed to encoding used in the propositional formula, where a modal- ity with a variable is expanded to a sequence of explicit conjunctions or disjunc- tions. More experiments are needed to determine whether the succinctness of value-passing formula does indeed have an impact on performance.

2000

"... In PAGE 11: ... Table1 . Performance of propositional and value-passing model checkers 4 Conclusions and Future Work We showed how the power of logic programming for handling variables and sub- stitutions can be used to implement model checkers for value-passing property logics with very little additional e ort and performance penalty.... ..."

Cited by 4

### Table 2 we give a complete proof system for propositional logic. The signal insertion operation

1996

"... In PAGE 11: ... Table2 : A proof system for propositional logic. cq assigns propositional formulae to the states contained in frames.... In PAGE 11: ...2) and the axioms given in Table 3. Additionally, we can use identities = i $ is provable from the axiom schemas and the inference rule given in Table2 . The axioms in Table 3 express that signal insertion to a frame is tantamount to signal insertion to all states of that frame (axioms (Ins1), (Ins5), (Ins6) and (TIns1)).... ..."

Cited by 7

### Table 2. Flat Propositional Contrastive Logic: Semantics

"... In PAGE 48: ... The syntax of CL1 is presented in Table 1. I now turn to the semantic de nition of CL1, presented in Table2 . I use `j= apos; to ambiguously denote satisfaction both of a classical propositional formula over one world, and for the satisfaction of a contrastive formula over two worlds, leaving the distinction to context.... In PAGE 126: ...Strong Cut-Elimination for Constant Domain First-Order S5 name of condition de nition general for every n, n is accessible from reverse for every n, is accessible from n re exivity is accessible from transitivity if is a proper initial segment of , then is accessible from universal any label is accessible from any label Table 1. conditions on accessibility logic Conditions on Accessibility K, KD general KT general, re exivity KB, KDB general, reverse3 KTB general, re exivity, reverse K4, KD4 general, transitivity S4 (= KT4) general, re exivity, transitivity S5 (= KTB4) universal Table2 . accessibility conditions for various logics label is available on a branch, if it occurs on that branch.... In PAGE 126: ... 402)), namely: L2 X; ( ; 2A) ! Y ` X; ( ; A) ! Y for any accessible from provided (i) for K; KB; and K4; must be available on the branch; (ii) for KD; KT; KDB; KTB; KD4; S4; and S5; must either be available on the branch or must be a simple, unrestricted extension of R2 X ! ( ; 2A); Y ` X ! ( ; A); Y provided is a simple, unrestricted extension of The tableau rules for _, :, 8 and the structural rules mon and cut remain unchanged. If S is any system listed in Table2 , let TQS be the tableau presentation of its constant domain rst-order extension. If we try to reuse the proof of strong cut-elimination for TQS5 in order to establish strong cut-elimination for TQS, we have to be careful, since both R2 and L2 come with complex side conditions.... ..."

### Table 4: Formulas we model checked for Fischer apos;s protocol. zero one is an atomic proposition that is true when there are less then two processes in lCS. one is an atomic proposition that is true when exactly one process is in lCS.

1999

Cited by 14