### Table 1: Complexity of model checking for default logic

1999

"... In PAGE 4: ... The above property and Theorem 6 also imply p 2- completeness of model checking for prerequisite-free dis- junctive default theories. In Table1 we summarize the complexity results de- scribed in this section. Each column of the table corre- sponds to a di erent condition on the conclusion part of default rules.... In PAGE 6: ... From the computational viewpoint, it turns out that Liberatore and Schaerf apos;s notion of model checking is harder than the one presented in this paper. In fact, comparing Table1 with the results reported in [Liber- atore and Schaerf, 1998], it can be seen that our for- mulation of model checking is computationally easier in almost all the cases examined, with the exception of nor- mal and supernormal default theories, for which the com- plexity of the two versions of model checking is the same. 6 Conclusions In this paper we have studied the complexity of model checking in several nonmonotonic logics.... ..."

Cited by 1

### Table 1. Test models

2005

"... In PAGE 3: ... The bifurcation diagram shows hysteresis. 3 EXAMPLES We have tested the discovery tool on a variety of example models that are listed in Table1 . Figure 1 shows the progress of the fitness in a typical optimization run for locating a Hopf bifurcation.... ..."

### Table 1: Some popular conditional probability distributions. If a node has both discrete and continuous parents, we can create a mixture distribution.

1999

"... In PAGE 1: ... In Section 6, we explain our varia- tional approximation, in Section 7 we introduce our new approach to handling evidence, in Section 8 we discuss the computational complexity of inference in hybrid BNs, and in Section 9, we present some experimental results to assess the quality of our approximation. 2 CPDs for hybrid networks For any directed graphical model, we must define the con- ditional distribution of each node given its parents: see Table1 for some examples. For discrete nodes with discrete parents, the simplest rep- resentation is a table (called a Conditional Probability Ta- ble, or CPT), which defines Pr(R = ijQ = j) def = ij.... ..."

Cited by 33

### Table 1: Posterior distribution of k for the 3 data sets based on a mixture model with random and default parameter values.

1994

"... In PAGE 10: ... In all the runs, the number of components never exceeded 24, hence the chosen value of kmax was inconsequential. Estimated posterior probabilities are given in Table1 . In each of the data sets, it is immediately apparent that there are a number of competing explanations of the data which are tenable.... In PAGE 18: ... Similar plots were obtained for the other data sets. Proportions of accepted `split or combine apos; moves vary between 8% and 14% ( Table1 ). For dimension changing moves, these proportions are satisfactory and show that our proposal based on adjacency is sensible.... ..."

Cited by 2

### Table 1: Posterior distribution of k for the 3 data sets based on a mixture model with random and default parameter values.

1994

"... In PAGE 10: ... In all the runs, the number of components never exceeded 24, hence the chosen value of kmax was inconsequential. Estimated posterior probabilities are given in Table1 . In each of the data sets, it is immediately apparent that there are a number of competing explanations of the data which are tenable.... In PAGE 18: ... Similar plots were obtained for the other data sets. Proportions of accepted `split or combine apos; moves vary between 8% and 14% ( Table1 ). For dimension changing moves, these proportions are satisfactory and show that our proposal based on adjacency is sensible.... ..."

Cited by 2

### Table 1: Posterior distribution of k for the 3 data sets based on a mixture model with random and default parameter values.

1994

"... In PAGE 10: ... In all the runs, the number of components never exceeded 24, hence the chosen value of kmax was inconsequential. Estimated posterior probabilities are given in Table1 . In each of the data sets, it is immediately apparent that there are a number of competing explanations of the data which are tenable.... In PAGE 18: ... Similar plots were obtained for the other data sets. Proportions of accepted `split or combine apos; moves vary between 8% and 14% ( Table1 ). For dimension changing moves, these proportions are satisfactory and show that our proposal based on adjacency is sensible.... ..."

Cited by 2

1994

"... In PAGE 10: ...Enzyme data : R = 2:86, = 1:45, = 0:122, = 2, g = 0:2, h = 1:22, = 1 Acidity data : R = 4:18, = 5:02, = 0:057, = 2, g = 0:2, h = 0:573, = 1 Galaxy data : R = 25:11, = 21:73, = 0:0016, = 2, g = 0:2, h = 0:016, = 1 Estimated posterior probabilities are given in Table1 . In each of the data sets, it is immediately apparent that there are a number of competing explanations of the data which are tenable.... In PAGE 16: ... Similar plots were obtained for the other data sets. Proportions of accepted `split or combine apos; moves vary between 8% and 14% ( Table1 ). For dimension changing moves, these proportions are satisfactory and show that our proposal based on adjacency is sensible.... ..."

Cited by 2

### Table 1. conditions on accessibility logic Conditions on Accessibility

"... In PAGE 48: ... is a CL1 formula. Table1 . Flat Propositional Contrastive Logic: Syntax 2 Propositional and rst-order Contrastive Logic 2.... In PAGE 125: ... We assume a binary relation of `accessibility apos; between labels. This relation may satisfy certain conditions, and a number of such conditions is de ned in Table1 . K and various extensions of K that can be dealt with by means of labelled tableaux require certain properties of accessibility between labels.... ..."

### Table 1. conditions on accessibility logic Conditions on Accessibility

"... In PAGE 9: ... We assume a binary relation of `accessibility apos; between labels. This relation may satisfy certain conditions, and a number of such conditions is de ned in Table1 . K and various extensions of K that can be dealt with by means of labelled tableaux require certain properties of accessibility between labels.... ..."

### Table 4. Implicit probability of default.

"... In PAGE 7: ...March 28, 2004 3:32 00007 Tools for the Analysis of Debt Problems 7 of the par oater is 1 = n X i=1 (r + S + rS) 1 (1 + r)i 1 (1 + )i + 1 (1 + r)n 1 (1 + )n + R n X i=1 1 (1 + r)i (1 + )i 1 = n X i=1 (r + + r ) 1 (1 + r)i 1 (1 + )i + 1 (1 + r)n 1 (1 + )n | {z } =1 +(S + rS + R r ) n X i=1 1 (1 + r)i 1 (1 + )i Upon cancellation of 1 on both sides, we obtain the coupon spread: S(1 + r) = (1 R + r) = S(1 + r) (1 R + r) that gives, once again, an implicit probability of default IPD = 1 + = S(1 + r) S(1 + r) + (1 + r R) : (4) Table4 presents the computations in Eq. (4) for di erent assumptions regarding recovery val- ues and spreads, given a risk free interest rate (similar tables can easily be computed with a di erent assumption on the risk free rate).... ..."