### Table 3: Comparison of monotone and non- monotone search in XRCE corpora.

"... In PAGE 5: ... In order to guar- antee a fast human interaction, in the remaining experiments of the paper, the mean iteration time is constrained to about 80 ms. Table3 shows the results using monotone search and combining monotone and non- monotone search. Using non-monotone search while the given prefix is translated improves the results significantly.... ..."

### Table 3: Comparison of monotone and non- monotone search in XRCE corpora.

"... In PAGE 5: ... In order to guar- antee a fast human interaction, in the remaining experiments of the paper, the mean iteration time is constrained to about 80 ms. Table3 shows the results using monotone search and combining monotone and non- monotone search. Using non-monotone search while the given prefix is translated improves the results significantly.... ..."

### Table 7: Monotonicity of linear terms

1994

"... In PAGE 12: ...3 Computing monotonicity of X in r We now give an inductive de nition of the monotonicity of X in r which is used as the basis of an algorithm for checking the monotonicity. We use mutually recursive de nitions ( Table7 and 8) to compute when r is mono- tone, and when r is anti-monotone. The de nitions state which variables occurring in r that must be determined before r is monotone (Mr), and which variables in r which must be determined before r is anti-monotone (Ar).... In PAGE 12: ... Let t be a linear term. The sets St (shrinking) and Gt (growing) are two sets of variables de ned by Table7 . The intuition being that if all variables in St (Gt) are determined (constants), then t takes on decreasing (increasing) values.... ..."

Cited by 24

### Table 1. Strongly monotone constraints.

"... In PAGE 4: ... Thus, our study fo- cuses on strongly monotone constraints, in the sense that they depend exclusively on the properties of the itemset and not on the underlying transaction database. For example, Table1 ) shows some data independent monotone constraints. In the rest of this article, we write, for the sake of brevity, monotone and antimonotone instead of strongly monotone and strongly antimonotone respectively.... ..."

### Table 7: Monotonicity of linear terms

"... In PAGE 13: ...3 Computing monotonicity of X in r We now give an inductive de nition of the monotonicity of X in r which is used as the basis of an algorithm for checking the monotonicity. We use mutually recursive de nitions ( Table7 and 8) to compute when r is mono- tone, and when r is anti-monotone. The de nitions state which variables occurring in r that must be determined before r is monotone (Mr), and which variables in r which must be determined before r is anti-monotone (Ar).... In PAGE 14: ... Let t be a linear term. The sets St (shrinking) and Gt (growing) are two sets of variables de ned by Table7 . The intuition being that if all variables in St (Gt) are determined (constants), then t takes on decreasing (increasing) values.... ..."

### Table 2: Monotonicity of linear terms

"... In PAGE 15: ...et t be a linear term, e.g. a sum composed of linear products, and (x) be a function such that (n) = ;, where n is a number, and (v) = fvg, where v is a variable. In Table2 two sets of variables, St and Gt, are de ned such that if all variables in St (Gt) are determined in , then t t 0 (t t 0) for any 0 such that v 0.... ..."

### Table 8: Performance on echocardiograms: monotonicity.

### Table 1. Some a-monotone constraints

"... In PAGE 3: ... A con- straint C is m-monotone if whenever a cell is in CUBE(C), so is every super-cell. Table1 lists some known a-monotone constraints. By re- placing with , or replacing with , a-monotone con- straints become m-monotone, and m-monotone constraints become a-monotone.... ..."

### Table 7: Monotonicity of linear terms r

1994

"... In PAGE 12: ...3 Computing monotonicity of X in r We now give an inductive de nition of the monotonicity of X in r which is used as the basis of an algorithm for checking the monotonicity. We use mutually recursive de nitions ( Table7 and 8) to compute when r is mono- tone, and when r is anti-monotone. The de nitions state which variables occurring in r that must be determined before r is monotone (Mr), and which variables in r which must be determined before r is anti-monotone (Ar).... In PAGE 12: ... Let t be a linear term. The sets St (shrinking) and Gt (growing) are two sets of variables de ned by Table7 . The intuition being that if all variables in St (Gt) are determined (constants), then t takes on decreasing (increasing) values.... ..."

Cited by 24

### Table 2: (non-)monotonicity under count

"... In PAGE 21: ...ogether (cf. the argument in the previous example). On the other hand, sentence (35b) is not true in this situation, simply because all the students drank a whole glass of beer together. Table2 summarizes the (non-)preservation of monotonicity properties under count for the nine classes of determiners according to the monotonicity of their two arguments. Note again that for each of the two classes #MON quot; and quot;MON#, there is an exception to the result that is mentioned in the table: the PTRIV deter- miners.... ..."