### TABLE 4. Assignments of Truth Values to the Atomic Propositions in AP Atomic Propositions State

### Table 1: Proof system PALPA with , , formulas in LPAL(PA), a some agent in A and p some propositional atom in P.

2007

### Table 1. Knowledge representation for an atomic proposition p in a state s Definition 3 An Abstract Kripke Structure (AKS) is a tuple A = hAP;S;S0;L;R;Fi. S;S0;R;F are defined as above and L : S ! 2Lit, Lit is the union of the set of positive atomic propositions and the set of negative atomic propositions.

"... In PAGE 3: ... The difference is that in our case the four values are used to represent a state information. Table1 summa- rizes the information contained in each of the four values.... ..."

### 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

### TABLE II Propositional rules for signed #0B-formulae, #0C-formulae, and literals #28p is an atomic formula#29.

### 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 3: Complexity results for propositional counterfactual evaluation

"... In PAGE 15: ... 4 Overview and discussion of results In this section we summarize and discuss our results and indicate possible extensions that we are currently investigating. The main results of this paper are compactly presented in Table3 . Di erent methods according to the di erent change semantics for evaluating a counterfactual p gt; q over a propositional knowledge base correspond to di erent rows in this table.... In PAGE 17: ... The model-based methods, however, all become polynomial under these restrictions and allow counterfactual evaluation even in O(kT k kqk) time in this case. Note that the theorems presented in the following sections often state yet more acute results than the ones shown in Table3 . For instance, we show that most hardness and completeness results hold even in case T is literal base, i.... In PAGE 17: ...ompleteness results hold even in case T is literal base, i.e. T consists of a set (or con- junction) of atoms or negated atoms. All results presented in Table3 are new except the P 2 -completeness of Ginsberg apos;s ap- proach for the general case. The latter has recently been shown by Nebel in [45].... ..."

### Table 2 shows results for randomly generated formulae [5], showing the effects of each of the three major extensions that we propose. It should be noted that working on simpler formulae and smaller automata offsets most of the additional cost of minimiza- tion. One can see from Table 2 that the reduction in transitions and fair sets corresponds to an increase in the number of terminal automata. Though we do not present a detailed analysis of the dependence of the results on the statistics of the formulae (number of nodes, number of atomic propositions, and percentage of temporal operators), we have observed the same trends reported in [5].

2000

"... In PAGE 15: ... Table2 . Results for 1000 random formulae with parse graphs of 15 nodes, using 3 atomic propo- sitions, and uniform distribution of the operators (CN, CM, CG , CD , CA ) for the internal nodes.... ..."

Cited by 1

### Table 2 shows results for randomly generated formulae [5], showing the effects of each of the three major extensions that we propose. It should be noted that working on simpler formulae and smaller automata offsets most of the additional cost of minimiza- tion. One can see from Table 2 that the reduction in transitions and fair sets corresponds to an increase in the number of terminal automata. Though we do not present a detailed analysis of the dependence of the results on the statistics of the formulae (number of nodes, number of atomic propositions, and percentage of temporal operators), we have observed the same trends reported in [5].

2000

"... In PAGE 15: ... Table2 . Results for 1000 random formulae with parse graphs of 15 nodes, using 3 atomic propo- sitions, and uniform distribution of the operators (CN, CM, CG , CD , CA ) for the internal nodes.... ..."

Cited by 1

### Table 11: Functions f; h and probabilistic function composition h f. 3.4 Probabilistic Semantics A condition is a set of sets of literals (or equivalently a propositional formula in disjunctive normal form) whose atoms are of the form g(x; y; cf) with cf being a real number in the interval [0; 1]. The set of all conditions is denoted by C. We restrict ourselves to bag functions of the following types f : X ! B(Y C)

1994

Cited by 2