### Table 1. Basic logics, axiomatic characterisations, and L-accessibility .

1997

"... In PAGE 5: ... A world w 2 W is idealisable if it has a successor in W. To illustrate the modularity of our method we concentrate on the ve basic axioms known as (T) 2A ! A, (D) 2A ! 3A, (4) 2A ! 22A, (5) 3A ! 23A, (B) A ! 23A, and the 15 extensions of the basic propositional normal modal logic K obtained as shown in the rst two columns of Table1 . The following properties of the reachability rela- tion R characterise these axioms, (T): re exivity, (D): seriality, (4): transitivity, (5): euclideanness, and (B): symmetry; see [11] for details.... In PAGE 5: ... We therefore obtain: De nition 8. For any logic L from Table1 , hW; Ri is an L-frame if each axiom of L is valid in hW; Ri. A model hW; R; V i is an L-model if hW; Ri is an L-frame.... In PAGE 5: ... De nition 9. Given a logic L and a set ? of strongly generated ground labels with root = 1, a label 2 ? is L-accessible from a label 2 ?, written as , if the conditions set out in Table1 are satis ed. A label 2 ? is an L-deadend if no 2 ? is L-accessible from .... ..."

Cited by 36

### Table 2: Basic logics, axiomatic characterisations, and L-accessibility .

1997

"... In PAGE 7: ... An axiom A is valid in a frame hW; Ri, i every formula instance of it is valid in hW; Ri. The rst two columns of Table2 show the axiomatisations of the 15 basic logics that can be formed from the axioms shown in Table 1. De nition 10 Given one of the logics L listed in Table 2, a frame hW; Ri is an L-frame if each axiom of L is valid in hW; Ri.... In PAGE 7: ... The rst two columns of Table 2 show the axiomatisations of the 15 basic logics that can be formed from the axioms shown in Table 1. De nition 10 Given one of the logics L listed in Table2 , a frame hW; Ri is an L-frame if each axiom of L is valid in hW; Ri. A model hW; R; V i is an L-model if hW; Ri is an L-frame.... In PAGE 7: ... We formalise this as follows. De nition 11 Given a logic L and a set ? of strongly generated ground labels with root = 1, a label 2 ? is L-accessible from a label 2 ?, written as , if the conditions set out in Table2 are satis ed. A label 2 ? is an L-deadend, if no 2 ? is L-accessible from .... In PAGE 26: ... Proof: Similar to the case of con- ditions (K), (4) and (4r) we prove by induction that for all such that [ ] 2 W there is a formula X : : : 2B 2 X , which then, using the same argument as above for the (T) condition implies [ ] j= B. By checking Table2 , it becomes obvious that the sub-conditions for box- formulae that apply to an L-Hintikka set, indeed imply: if [ ] 2 W and , then [ ] j= B. A = 3B: According to condition 6 in the de nition of Hintikka sets, there is a formula X : : :n : B 2 X .... ..."

### Table 2: Dice-game requirements characterised with domain terms (weighed by relevance)

"... In PAGE 3: ... In our work, we focus on nominating lexically and syntactically interesting concepts to become members of a list of domain terms characteristic to each requirement. Table2 and Table 3 show a number of simple requirements statements drawn from the Dice Game (D1 to D7) and the Coin Game (C1 to C7) systems. Each statement can be characterised with a list of standardised domain terms, which were selected from their text.... In PAGE 4: ... A simpler approach could rely on the use of a domain thesaurus able of cross- referencing similar terms. Terms extracted from the requirements text of two gaming systems (see Table2 and Table 3) clearly illustrate the potential semantic disparity between requirements documents.11 Since both documents belong 11 Such disparity in small requirements documents may not present any problems to an experienced analyst, who would immediately identify an opportunity to abstract the required system functions into a description of a more general problem.... In PAGE 7: ... The domain-mapping thesaurus is used to translate problem domain keywords into solution domain facets. Consider a single requirement for the dice game system (see Table2 ), i.e.... ..."

### Table 3: Coin-game requirements characterised with domain terms (weighed by relevance)

"... In PAGE 3: ... In our work, we focus on nominating lexically and syntactically interesting concepts to become members of a list of domain terms characteristic to each requirement. Table 2 and Table3 show a number of simple requirements statements drawn from the Dice Game (D1 to D7) and the Coin Game (C1 to C7) systems. Each statement can be characterised with a list of standardised domain terms, which were selected from their text.... In PAGE 4: ... A simpler approach could rely on the use of a domain thesaurus able of cross- referencing similar terms. Terms extracted from the requirements text of two gaming systems (see Table 2 and Table3 ) clearly illustrate the potential semantic disparity between requirements documents.11 Since both documents belong 11 Such disparity in small requirements documents may not present any problems to an experienced analyst, who would immediately identify an opportunity to abstract the required system functions into a description of a more general problem.... ..."

### Table 7 : Characterising integrated models

### Table 1. Comparison of characterisations

2001

"... In PAGE 35: ...We now try to provide an intuitive understanding of the technical differences between the characterisations of termination we have proposed. These are sum- marised in Table1 . Note that simply-acceptability is a special case of P-simply- acceptability that does not need to be distinguished in this context.... ..."

Cited by 4

### Table 1 - Devices Characterisation

"... In PAGE 17: ... The application often implies a particular device. A number of types of devices (or device scenarios) have been identified in Table1 . Characteristics of devices include: portability/wearability [Fort02], human interface, modes of communication (text, voice, image etc), cost of ownership and use, power requirements, processing power, range of data applications, locations it can be used, social acceptability, etc.... ..."

### Table 6(a): Multiple regression model for normalised residential burglary rate.

2005

"... In PAGE 20: ...258) and street crime (adjusted R2=0.636) and are statistically significant as detailed in Table6 . The differences in R2 values for each crime type reflect the relative strength of the Spearman correlations.... In PAGE 21: ... Table6 (b): Multiple regression model for normalised street crime rate. (a) (b) ... ..."

### Table 11 Strong Monads

"... In PAGE 42: ...) Now a ?-autonomous category with ( nite and nullary) products and co- products (one implies the other because of the duality) is a model of classical linear logic; for convenience, we call the product N and the coproduct . We add to this the following: Definition 13 (Strong Monads) A strong monad is a monad h ( ); ; i on C, together with a natural transformation : ( ) ! ( ) such that the diagrams in Table11 commute.... 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 Table11 , 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.... In PAGE 50: ...and y commutes because of the bottom diagram in Table11 . (The small triangles commute by de nition.... ..."

### Table 11 Strong Monads

"... In PAGE 40: ...) Now a ?-autonomous category with ( nite and nullary) products and co- products (one implies the other because of the duality) is a model of classical linear logic; for convenience, we call the product N and the coproduct . We add to this the following: Definition 13 (Strong Monads) A strong monad is a monad h ( ); ; i on C, together with a natural transformation : ( ) ! ( ) such that the diagrams in Table11 commute.... In PAGE 46: ... 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 Table11 , 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.... In PAGE 47: ... A A0 f f0/ / amp; amp; L L L L L L L L L L ( B) B0 ( g) g0 / / tB;B0 ? ( C) C0 C IdC0 / / t C;C0 ( C) C0 tC;C0 / / (C C0) (B B0) (g g0) / / apos; apos; O O O O O O O O O O O ( C C0) tC;C0 y (C C0) C C0 6 6 m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m The top edge is the C-morphism corresponding to (g f) (g0 f0), whereas the composite of the bottom two edges is the C-morphism corresponding to (g g0) (f f0). However, ? commutes because t is a natural transformation, and y commutes because of the bottom diagram in Table11 . (The small triangles commute by de nition.... ..."