### Table 3: Reductions and expansions for proof circuits two morphisms are equal if their expanded normal forms are equal. In fact, in this case this is quite trivial due to not having thinning links, and essentially amounts to the traditional technique of Kelly{Mac Lane graphs, as shown in [B92], where the coherence question for various theories of monoidal categories was solved using this approach.

"... In PAGE 29: ... 7 Proof circuits We now introduce proof circuits for the context calculus. The basic links are given in Table 2, with corresponding rewrites in Table3 . The following comments ought to be taken in conjunction with the gures in these Tables.... In PAGE 29: ... In Table 2 we illustrate only the binary case of this duplication node. In Table3 we have a number of rewrites involving duplication; although we illustrate only the binary cases, the reader ought to keep in mind that there are similar rewrites for the n-ary versions. (Actually, one could make do with a binary node only, and use the binary rewrites to simulate the n-ary nodes, but it is simpler to use n-ary nodes.... ..."

### Table 2. Constraints in traditional graph drawing.

"... In PAGE 4: ...2 Input Dependent Constraints The constraints in the previous section did not depend on the input. Input dependent constrains that are commonly used in traditional graph drawing [5, 13, 25] are listed in Table2 . Next we discuss the possibility to apply these traditional drawing constraints to the layouts of sequence diagrams.... In PAGE 4: ... Next we discuss the possibility to apply these traditional drawing constraints to the layouts of sequence diagrams. The first constraint in Table2 describes a need to place a given set of vertices to the center of the drawing. This need is justified since the center of a drawing is usually the most important and prominent place where vertices can be placed.... ..."

### Table 4. An examination timetabling by the graph theory

"... In PAGE 7: ...Table4 also shows the final solution obtained by the graph theory. A1 1 4 3 8 7 2 5 6 A2 6 4 3 2 1 7 8 5 A3 1 2 4 3 5 6 7 8 A4 8 7 6 1 4 2 3 5 Fig.... ..."

### Table 5: Comparing Traditional Theories of Gatekeeping with the Meta-theory of Network Gatekeeping

"... In PAGE 14: ... We have identified a compound process of gatekeeping on the Internet. To complete the process of developing a meta-theoretical framework, we compare and analyze the differences between traditional gatekeeping and network gatekeeping ( Table5... ..."

### Table 4. Commonly used aesthetic criteria for traditional graph drawing.

### 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 1 - Differences Between Traditional Systemic Thinking and

"... In PAGE 3: ...Figure 1 provides a graph of the historic returns and risk for different asset classes from 1970 to 1994. Table1 presents the data for each asset class. Figure 1 plots such assets as small-cap stocks, mid-cap stocks, S amp;P 500 stocks, gold, intermediate corporate and government bonds, long term government bonds and 90 day treasury bills.... ..."