### Table 1: Prediction whether three-premise arguments or one-premise arguments should be judged stronger for each model across the three conditions.

### TABLE I Number of m-premise arguments based on five objects and 1

### Table 2 are also L cool. The path restrictions are easily checked. In the second rule, the dangerous variable y occurs in a wild argument of the target, and not in the left-hand side of the premise. In the fourth rule, the dangerous variable y is the target, and does not occur in the left-hand side of the premise.

"... In PAGE 14: ... Regular expressions can also include two special constants 0 and 1, which we do not take into account for the sake of simplicity; the 1 would require a reformulation of the transition rules for BPA in Table 1. The behaviour of the binary Kleene star is captured by the four transition rules in Table2 . Recall that if we take the rst argument of sequential composition to be wild, and both arguments of alternative composition and the second argument of sequential composition to be tame, then the transition rules for BPA are L cool.... In PAGE 14: ... Table2 : Transition Rules for the Binary Kleene Star Corollary 4.1 Language preorder is a precongruence with respect to BPA .... ..."

Cited by 5

### Table 2 are also L cool. The path restrictions are easily checked. In the second rule, the dangerous variable y occurs in a wild argument of the target, and not in the left-hand side of the premise. In the fourth rule, the dangerous variable y is the target, and does not occur in the left-hand side of the premise.

"... In PAGE 14: ... Regular expressions can also include two special constants 0 and 1, which we do not take into account for the sake of simplicity; the 1 would require a reformulation of the transition rules for BPA in Table 1. The behaviour of the binary Kleene star is captured by the four transition rules in Table2 . Recall that if we take the rst argument of sequential composition to be wild, and both arguments of alternative composition and the second argument of sequential composition to be tame, then the transition rules for BPA are L cool.... In PAGE 14: ... Table2 : Transition Rules for the Binary Kleene Star Corollary 4.1 Language preorder is a precongruence with respect to BPA .... ..."

Cited by 5

### Table 3: Transition Rules for Iteration In view of the procedure in Section 3.2 we take the argument of iteration to be tame. Furthermore, as before, the rst argument of sequential composition is wild, and the arguments of alternative composition and the second argument of sequential composition are tame. It is not hard to see that the TSS for BPA with iteration is RBB safe with respect to this tame/wild labeling. Note that in the second transition rule in Table 3, the right-hand side y of the premise occurs in a wild argument of the target.

2000

"... In PAGE 11: ... The iteration operator [25], denoted by t , either terminates successfully or exe- cutes t t . Two transition rules for iteration are presented in Table3 , which are added to the transition rules for BPA in Table 1. The resulting TSS for BPA is in path format, and since it does not involve negative premises it is complete.... In PAGE 11: ...7 Rooted branching bisimulation is a congruence with respect to BPA with iteration. The transition rules in Table3 are not RBB cool. Namely, in the second transition rule for iteration, the iteration operator occurs in the target y x , and the argument of the source x occurs is the left-hand side of the premise, so the RBB cool format requires that there exists a patience rule for the argument of iteration.... In PAGE 11: ... Namely, in the second transition rule for iteration, the iteration operator occurs in the target y x , and the argument of the source x occurs is the left-hand side of the premise, so the RBB cool format requires that there exists a patience rule for the argument of iteration. However, such a patience rule is not present in Table3 nor in Table 1. 3.... ..."

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### Table 8 Premise triples along with the target categories for the items of Experiment 4

"... In PAGE 18: ... The difference between similarity conditions was the category term in the premise of the argument. Table8 presents the 24 cat- egories used and Table 9 a sample item from each Similarity by Centrality condition. Like in Experiments 1 and 2, relative centrality was defined by manipulating the number of properties depending on a feature.... ..."

### Table3.Premiseinvestigationsupportedbydatastrategy. Premises

2001

### Table 3: Various models that apply to the arguments shown in Table

"... In PAGE 5: ... Let reasoner R be given. Suppose that just the models m 1 - m 7 of Table3 come to R apos;s mind when thinking about #28A #03 #29, and that R can determine the truth-values of formulas #281#29a and #281#29b in each of these models. Then, in view of #283#29b, the subset of m 1 - m 7 satisfying the premises of #28A #03 #29 is not empty.... In PAGE 10: ... Within the mental models perspective, it is natural to speculate that the respondents took the contradictory con- clusion to be true in the models of the premise, and the valid conclusion to be false. We tested this hypothesis by presenting students with models m 1 - m 5 in Table3 , and requesting them to select which of the two sentences #282#29c,d is true in each. From the point of view of logic, since m 1 - m 5 satisfy the premise #282#29a, each satisfy its logical consequence #282#29c and not the negation #282#29d.... In PAGE 10: ... 11 So the latter formula is not simply a confusing means of expressing the former. Therefore nothing 11 Speci#0Ccally, m 6 of Table3 satis#0Ces 9x#28Lx _ _8y#28Dy#29#29 but not 9x#28Lx#29 _ _8y#28Dy#29.... In PAGE 26: ... #0F There is no one such that either he lives tomorrow or else everyone dies tomorrow. Figure 2: The problem corresponding to m 1 in Table3 . The order of the two conclusions was individually randomized for each subject.... ..."

### Table 1: Moods involved in traditional syllogisms.

2007

"... In PAGE 19: ... Let us summarize briefly some facts about classical syllogisms. A syllogism is a two premise argument that consists of three out of four sentence types, or moods ( Table1 ). The order of the predicates involved is regimented by the four figures (Table 2).... ..."

### Table 1: Inference rules and propagation rules for the probabilities in the premises (0 x 1, 0 y 1) to the coherent probability (z) of the conclusion. The rules above the line (rw = right weakening) are valid in system p and probabilistically informative. The arguments below the line (tr=transitivity, mb=modus barbara, an-c=an-contraposition, na-c= na-contraposition) are neither valid in system p nor probabilistically informative (i.e., only the unit interval, [0;1], can be inferred). j=X!Y means X!Y is a tautology. ^ (\and quot;), and : (\not quot;) are de ned as usual in classical logic. Column # refers to the present experiments.

in Abstract

"... In PAGE 2: ... 2 Experiment 1 Method and Procedure In Experiment 1 we investigated the cut and the right weakening rule of system p, and two forms of contraposition which are not valid in system p (cf. Table1 ). cut and right weakening are the nonmonotonic versions of transitivity, and are therefore of special interest.... In PAGE 4: ...ntervals. Practically all subjects clearly endorse the right weakening rule. To estimate the reliability of the data we calculated correlations between the responses in those tasks which have normatively equivalent bounds in the conclusions. The propagation rule of the normative lower bound of the cut rule is commutative (xy = yx, see Table1 ). There are two pairs of tasks in which the percentages in the premises are interchanged (tasks B2 and B5, and B9 and B11, respectively).... ..."