### Table 1 displays all of the special notations for semantic, proof-theoretic, and computational relations. The precise meanings and applications of these notations are developed at length in subsequent sections. The no- tation described above is subscripted when necessary to distinguish the logical and computational relations of di erent systems.

"... In PAGE 7: ... Table1 . Special Notations for Logical and Computational Rela- tions 2 Specifying Logic Programming Languages Logic typically develops its `principles and criteria of validity of inference apos; by studying the relations between notations for assertions, the meanings of those assertions, and derivations of notations expressing true assertions.... ..."

### Table 1. Sequence of Drug Treatments and Subject Assignment

"... In PAGE 12: ... The food and cocaine components continued to alternate during a daily session until each component was presented three times. The sequence of drug treatments and subject assignment for the entire study are shown in Table1 . The 6 subjects were assigned to overlapping protocols to ensure that N=4 for each experimental condition.... ..."

### Table 5: Average number of rounds required to reach agreement, by treatment and size of the pie.

"... In PAGE 13: ... This brings us to the issue of the speed at which agreement is reached in the different treatments. Table5 shows the average numbers of rounds required to reach agreement. With the small pie, averages in all treatments are not significantly different.... ..."

### Table 1. The areas of proof theory, organized by goals.

2001

"... In PAGE 8: ... I first present a very quick overview of the present goals of proof theory. Table1 gives a three-fold view of proof theory, in which proof theory is split into three broad categories based on the goals of the work in proof theory. The first column represents the traditional, classic approaches to mathe- matical proof theory: in this area the goal has been to understand stronger and stronger systems, from second-order logic up through higher set the- ories, and especially to give constructive analyses of the proof-theoretic strengths of strong systems.... ..."

Cited by 3

### Table 1. The areas of proof theory, organized by goals.

2001

"... In PAGE 8: ... I rst present a very quick overview of the present goals of proof theory. Table1 gives a \three-fold quot; view of proof theory, in which proof theory is split into three broad categories based on the goals of the work in proof theory. The rst column represents the traditional, classic approaches to mathe- matical proof theory: in this area the goal has been to understand stronger and stronger systems, from second-order logic up through higher set the- ories, and especially to give constructive analyses of the proof-theoretic strengths of strong systems.... ..."

Cited by 3

### Table A: MP2000 Field Test Assigned Cases and Field Outcomes by Instrument Treatment

### Table 1: Treatment-Control Differences at Baseline by Assignment Status, Selected Variables

"... In PAGE 10: ...) Moulton (1990) provides a nice illustration of inference problems that can arise from ignoring correlated errors. Table1 reports the mean of several baseline characteristics for the treatment and control groups for the full sample, separately for Black and Latino students, and disaggregated by cohort for Black students. Because random assignment was implemented within strata, regressions were estimated to condition on the 30 original randomization strata, and conditional treatment-control differences and t-tests are reported as well.... In PAGE 11: ... Unless otherwise noted, we utilize the revised weights that Mathematica recommended on April 3, 2003 throughout this paper. The results in Table1 suggest that the assignment groups were well balanced, as one would expect with random assignment. One exception, however, is the oldest cohort of African American students.... In PAGE 22: ...pattern of cohort effects, although we find some tendency for older students to have a larger treatment effect when Kindergarten students are included in the sample and the cohort-treatment-status interaction is constrained to be linear. The treatment effect on the third-year composite test score for each cohort can be viewed in the Addendum at the bottom of Table1 . The treatment effects are not uniform, and it is particularly large for the 4th grade cohort, but they individually have large standard errors.... ..."

### Table 1: Sample breakdown between treatments and control and assigned versus actual participation

2001

"... In PAGE 11: ... IV. Baseline characteristics and attrition Table1 compares the randomized assignment with observed treatment status.14 There is perfect take-up for the voucher only case.... In PAGE 14: ...14 As we saw in Table1 , there is a potential problem of endogenous compliance with the training component. There may be some latent correlate of the outcome measure that influenced the choice to take up the program amongst those who are assigned access.... ..."

Cited by 1

### Table 1: Simplified example of point assignments in the bidirectional partner selec- tion treatment with four subjects

"... In PAGE 7: ... Subsequently, the spe- cific combination of pairs that maximizes the sum of mutual assignments is selected for implementation. The simplified example of Table1 with four group members A, B C and D might clarify the procedure. Entries of Table 1 are amounts of ECU allocated by a subject to each other subject.... In PAGE 7: ... The simplified example of Table 1 with four group members A, B C and D might clarify the procedure. Entries of Table1 are amounts of ECU allocated by a subject to each other subject. In the example, subject A allocates 10 to B, 5 to C, and 10 to D; subject B allocates 20 to A, 8 to C and 7 to D; and so on.... In PAGE 24: ...Table1 0: Frequencies of intentions to be paired with a particular type in each bidi- rectional mechanism Type Mechanism number Own Preferred Subject 1st 2nd 3rd 4th 5th Total c c 1 2 5 8 9 25 c m 1 1 2 1 0 5 c f 0 0 0 0 0 0 m c 4 4 6 7 5 26 m m 12 10 9 7 5 43 m f 1 1 0 0 0 2 d c 2 1 2 1 2 8 d m 5 7 1 2 3 18 d f 1 3 0 0 0 4 c - 1 0 0 0 2 3 m - 2 3 5 2 7 19 f - 5 3 5 7 3 23 c indifferent 0 0 0 0 0 0 m indifferent 1 1 1 1 0 4 f indifferent 0 0 0 0 0 0 sum 36 36 36 36 36 180 Note: c denotes cooperator, m represents middle range contributor and f denotes free-rider. whereas the last pair of this category was matched residually.... In PAGE 25: ...Table1 1: Proportion of cooperators and free-riders being indifferent to random matching in the unidirectional and bidirectional partner selection mech- anisms Unidirectional Bidirectional Mechan. Cooperators Free riders Cooperators Free riders nr.... ..."

### Table 1 Sequent Calculus Rules for S4

"... In PAGE 5: ... More abstractly formu- lated, we will have what can be described category-theoretically as a monad, or proof-theoretically as an S4 modal operator. We should recall that S4 modalities are given by the rules in Table1 ; classically or intuitionistically, these rules give the usual modal logic [34, Section 9.1], but they can equally well be added to linear logic and they satisfy the usual proof-theoretic properties (cut elimination and so on) [18].... In PAGE 8: ...Table 2 The System LL ?; A ` @L ?; @A ` ?; @A ` B; @R1 ?; @A ` @B; ? ` A; B; @R2 ? ` A; @B; ?; A ` B; L1 ?; A ` B; ?; A; @B ` L2 ?; A; @B ` ? ` A; R ? ` A; So we are led to consider modalities given by the rules in Table 2; we will call these strong modalities (the category-theoretic counterpart of (4) is called a strength). Conversely, the usual S4 rules ( Table1 ) will be called monoidal modalities (since (2) makes a monoid in an appropriate category of endofunc- tors).This system, based on classical linear logic together with a strong modality, will be called LL ; it will be our point of departure.... In PAGE 37: ... Proof We make an induction on the length of the proof of ` ; we go by cases according to the last rule of the proof. We use a presentation of our basic system, LL 00, given in Table1 0; we can easily prove a dual form of Proposition 9 to show that they are equivalent to the rules of Table varModalRules. Axiom The sequent is of the form A ` A, so the result is clear.... In PAGE 48: ... The top diagram, for example, expresses the equality A A = A A; now the rst is given by the proof Ax A A ` A R A ` A L A ` A L A ` A A A ` A cut A ` A whereas the second is given by the proof AxA A ` A R A ` A L A ` A L A ` A R A ` A L A ` A A A ` A cut A ` A We want these two proofs to be equal. We need similar equalities for the other diagrams in Table1 1, and for the other diagrams de ning a ?-autonomous category. With this de nition of equality between proofs, then, we have de ned a category, F, in which the objects are linear logic formulae and in which the morphisms are proofs of entailments.... ..."