### 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 1: Infants apos; behaviour during the sensorimotor stage, with a description of their developing cognitive activity and the corresponding aspect of mathematics regarded as stemming from that activity.

"... In PAGE 4: ... The activities listed by MacLane can be identified within this description of behaviour. Table1 lists infants apos; behaviour at each stage between nought and two years, a suggested description of their developing cognitive activities and the corresponding portion of mathematics regarded as stemming from that activity, according to MacLane. The table suggests that within the first two years of life, humans begin to develop the cognitive activities which are required as a foundation to mathematical development.... ..."

### Table 1. Commercial Generalisation Technology

2003

"... In PAGE 9: ...1 Commercial availability of generalisation architectures Whilst generalisation remains largely a research topic for universities, there are a number of commercial vendors who provide varying levels of functionality. Table1 . categorizes and lists ... ..."

### Table 2 Generalised test model

"... In PAGE 5: ... In the generalised model probabilities are associated to the possible test results. For instance a good tester will detect a fault in the testing unit with a probability of pb0, and a fault will escape with a probability pb1 (pb0 + pb1 = 1) (see Table2 ). Similarly a faulty tester will report a good unit as good or faulty with probabilities pc0 and pc1, where pc0 + pc1 = 1, and so on.... ..."

### Table 3. Generalisation test results.

"... In PAGE 7: ... Again, a 100% solution was found. All results are summarised in Table3 . The exact training sets and some testing patterns used in the experiments are included in the Appendix.... ..."

### Table 3: Graph types

2007

"... In PAGE 7: ... If the graph is directed, the pair of nodes is ordered, so the graph can have edges from node A to node B as well as edges from B to A. These four combinations are speci ed by the values in Table3 . The return value is a new graph, with no nodes or edges.... ..."

### Table 1: Examples of generalisable competencies _______________________________________________

"... In PAGE 1: ...A further rationale for problem-based learning is that it supports the conditions for effective adult learning. The adoption of PBL can be expected to contribute to the competencies listed in Table1 if the design of tasks matches adult learning principles, or andragogy. Table 2 presents conditions for effective adult educator practices summarised from Brookfield (1988).... ..."

### Table 5. Deduction rules for generalised switches

2005

"... In PAGE 11: ...1 Symbolic Ingredients Given an STS with a switch relation !. We de ne a generalised switch relation =) L F(V [I) T(V [I)V L (see the deduction rules of Table5 ). The intuition behind this relation is that it abstracts from the unobservable events that possibly precede and follow an observable event.... ..."

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### Table 5{2: Generalised Hebb Rule

1993

"... In PAGE 50: ...60 0.16 6 - 163 149 7:4 Table5 {1: Maximum Spans for di erent Resetting Probabilities Figs 5{2 and 5{3 show the functions Q(R;; r) and S( ;;r) from the results of numerical analysis. The theoretical maximum span obtainable for a 512(9) net is apos; 163, which occurs when r =0:0016 and =6.... In PAGE 57: ....g. [Stanton amp; Sejnowski 89], that increases in synaptic strength, or Long-Term Potentiation (LTP), may be balanced by decreases in e cacy through Long-Term Depression (LDP) - although the results are often in debate [Willshaw amp; Morris 89]. However, it is possible to explore an abstract space of possibilities - for example [Palm 88] draws up a generalised framework for weight update rules (for continuous weighted nets) as shown in Table5 {2. In Palm apos;s formalism the variables w ; z correspond to real-valued weightchanges.... In PAGE 58: ... This would be achieved by converting the weight increments or decrements for real-valued weights into probabilities for triggering or resetting binary-valued weights. Then the variables in Table5 {2 would correspond to: w;; z = prob(w ij ! 1) x;; y = prob(w ij ! 0) The relevant probabilities for switches are shown schematically in Fig 5{9. Below are listed some of the particular values for the probabilities w ; z investigated:... In PAGE 64: ...0 0.17 6 178 168 7:3 Table5 {3: Maximum Spans for di erent Generalised Learning Methods smaller threshold of 6, the much better span of apos; 178 is obtained, with x =0:0875 ( 0:0025) instead. The following are worth noting: The prediction from Eq 5.... In PAGE 65: ... However, this may not be the case if patterns were correlated or pattern coding was less sparse. Palimpsest Scheme Optimal Parameters Span (approx) Random Resetting r =0:0016, z =1, =6 149 Weight Ageing r(A)=1$ A gt;1900 1,700 Generalised Learning x =0:088, z =1,w = y =0, =6 168 Table5 {4: Comparison of Palimpsest Schemes in WillshawNet 5.4 Summary All the palimpsest schemes discussed above, given certain choices of parameters, can allow a net to function as a short-term memory with a stable span.... ..."

### Table 2: Deduction rules for generalised parallel composition: S

1997

"... In PAGE 10: ... 4.3 Generalised parallel composition The generalised parallel composition operator is de ned by the deduction rules in Table2 . The parallel composition operator k is labelled by a set S of pairs of events.... In PAGE 11: ... However, the presence of the requirement out(i;; j;; m) before in(i;; j;; m)blocks the ex- ecution of in(i;; j;; m) as long as out(i;; j;; m) has not been executed. Thus, the only possible sequence of transitions is: in(i;; j;; m) k out(i;;j;;m)7 !in(i;;j;;m) out(i;; j;; m) out(i;;j;;m) ! in(i;; j;; m) k quot; in(i;;j;;m) ! quot; k quot;: Next, we explain the deduction rules from Table2 in more detail. Rule [HC 1] expresses that x k S y has the possibility to terminate if both x and y have.... ..."

Cited by 8