### Table 2 Framing Devices (search terms set in boldface, homonyms in orange, conditional searches in olive) On first sight, Qualrus appeared to be a prime candidate for our tasks. It is the most recently developed program, and boosts automatic coding functions, which is the reason why some have considered it most suitable to alleviate the Grounded Theory bias (Gibbs et al. [ 2003] 2002: 10). Yet, Qualrus turned out to be the least suited for our purposes. Its search functions are not comprehensive and efficient, if fairly speedy. Using the Q-Tools search menu in Qualrus, simple string searches were completed within 23 seconds over all

"... In PAGE 19: ... From the reading, we distilled five hypothesized frames based on two master frames and identified corresponding 71 lemmata, many of which can been found in a single search. Table2 displays the search terms with the actual search strings set in boldface. Automatic Coding Four types of searches were to be performed.... In PAGE 20: ... quot; These searches do not lend themselves to automatic coding, but require a case by case interpretation by the researcher. Ideally, simple, Boolean, and proximity searches would thus be coded automatically, while those searches that required user input (highlighted in orange in Table2 ) would display the context, in which the word is found to facilitate a swift identification of the proper code. None of the programs fulfilled all our requirements, but there were substantial differences in the ... ..."

### Table 1: Constructors in First-Order Description Logics

"... In PAGE 2: ... The for- mer are interpreted as subsets of a given domain, and the latter as binary relations on the domain. Table1 lists constructors that allow one to build (complex) concepts and roles from (atomic) concept names and role names.... In PAGE 3: ...Table 1: Constructors in First-Order Description Logics Description logics di er in the constructions they admit. By combining constructors taken from Table1 , two well-known hierarchies of description logics may be obtained. The logics we consider here are extensions of FL?; this is the logic with gt;, ?, universal quanti cation, conjunction and un- quali ed existential quanti cation 9R: gt;.... In PAGE 3: ... For instance, FLEU? is FL? with (full) existential quanti cation and disjunction. Description logics are interpreted on interpretations I = ( I; I), where I is a non-empty domain, and I is an interpretation function assigning subsets of I to concept names and binary relations over I to role names; complex concepts and roles are interpreted using the recipes speci ed in Table1 . The semantic value of an expression E in an interpretation I is simply the set EI.... In PAGE 4: ... First, item 1 is next to trivial. The semantics given in Table1 induces translations ( ) and ( ) taking concepts and roles, respectively, to formulas in a rst-order language whose signature consists of unary predicate symbols corresponding to atomic concepts names, and binary predicate symbols corresponding to... In PAGE 7: ... Hence, ALC lt; ALCR, ALCN, ALCRN. a Now, what do we need to do to adapt the above result for other exten- sions of FL? de ned by Table1 ? For logics less expressive than ALC we can not just use bisimulations, as such logics lack negation or disjunction, and these are automatically preserved under bisimulations; moreover, the proof of Theorem 3.3 uses the presence of the booleans in an essential way.... In PAGE 8: ...Table1 that are not in FL?, and examine which changes are needed to characterize the resulting logics. This is followed by a section in which we consider combina- tions of constructors.... In PAGE 20: ...7.6 Classifying an Arbitrary Description Logic To obtain a characterization of an arbitrary description logic (de ned from Table1 ), somply combine the observations listed in Sections 4.... In PAGE 20: ... Several comments are in order. First, the diagram does not mention all possible combinations of the constructors listed in Table1 . The reason for... ..."

### Table 2 Representation and integration according to the theory of mental models

2003

"... In PAGE 11: ... over the past two decades, quantified propositions are represented directly in terms of arbitrary individuals. For example, in the Bucciarelli and Johnson-Laird (1999) version of the theory, processing the premisses of AA1A (in non-canonical order) results in the suite of mental models shown in Table2 . Every line in a mental model represents an individual, so for the first premiss we have two individuals, which have the same properties, A and B.... In PAGE 12: ... This is done by trying to refute each of the preliminary conclusions by a counterexample: an extended model in which the premisses are still true but the conclu- sion is false. Such a counterexample can be found for All C are A (as shown in the last row of Table2 ) but not for All A are C , so only the latter survives and is spelled out as the final conclusion. One of the things critics of mental-model theory have complained about is that it is not quite clear what it is, not only because the theory has gone through so many revisions, but because its key tenets remain somewhat underspecified.... In PAGE 12: ... Usually, a version of the mental- model theory comes with one or more computer implementations and a description of what these programs do, but in general this does not suffice to pin down exactly what mental models are. To illustrate, while the first model in Table2 is said to represent the proposition All A are B , we are also told that the model in the third row verifies the proposition All C are A . The former claim suggests that individuals representing the subject term must be enclosed in square brackets, to encode that its representation is exhaustive; the latter suggests that this is not necessary.... In PAGE 12: ... Or consider the sentence Two A are B . How can we represent this in a mental model? One might think that the first model of Table2 is a plausible candidate, but this cannot be right, for two reasons at least. First, this model already represents the interpretation of All A are B , which is patently not synonymous with Two A are B .... ..."

Cited by 6

### Table 1: Correspondence Between MEBN and First-Order Logic Syntactic Elements

2003

"... In PAGE 8: ... The value of RV X when applied to instance V is written X(V); the expression X(V)=O denotes that RV X has outcome O when applied to instance V. Table1 shows the correspondence between the above MEBN syntactic elements and syntactic elements of first-order logic. Table 1 also shows MEBN constructs corresponding to logical connectives, nested function application, and quantification.... In PAGE 8: ... Table 1 shows the correspondence between the above MEBN syntactic elements and syntactic elements of first-order logic. Table1 also shows MEBN constructs corresponding to logical connectives, nested function application, and quantification. In first-order logic, logical connectives are used to compose terms into sentences.... ..."

Cited by 2

### Table 1: First functions and their orders for the method of iterated commutators

"... In PAGE 32: ...Table1 0: A Matlab program for the IC 4 GR for Toda #0Dows function L1 = TodaIC4_Radau#28L0, h, t0, tf#29; #25 function L1 = TodaIC4_Radau#28L0, h, t0, tf#29; #25 #25 Solves the Toda flow with the Lie group invariant IC4GR #25 B_IC4R#28L0, t1,t2,t3,t4,t5,t6#29 evaluates the 3-rd order interpolant #25 to B at t=t1,.... In PAGE 33: ...Table1 1: A Matlab program for the Magnus method with r = 2 and order 4 for Toda #0Dows function L1 = TodaMagnus4#28L0, h, t0, tf#29; #25 function L1 = TodaMagnus4#28L0, h, t0, tf#29; #25 #25 Solves the Toda flow with the Lie group invariant method Magnus4 #25 #28cf. Iserles and Norsett#29 #25 c1 = 1#2F2 - sqrt#283#29#2F6; c2 = 1#2F2 + sqrt#283#29#2F6; w11 = 1#2F2; w12 = 1#2F2; w21 = sqrt#283#29#2F6; for tn = t0 : h : tf-eps #25 #25 integrate the orthogonal flow #25 #5BX1, X2, Xh#5D = B_M4#28L0, c1*h, c2*h, h#29; Psi_h = h * #28w11*X1 + w12*X2#29; sigma0_h = Psi_h + 0.... In PAGE 34: ...Table1 2: A Matlab program for a 4-th order Lie-group method of Munthe-Kaas for Toda #0Dows function L1 = TodaMK4#28L0, h, t0, tf#29; #25 function L1 = TodaMK4#28L0, h, t0, tf#29 #25 #25 Solves the Toda flow with the Lie group invariant RK method RK4r.m c = #5B0 1#2F2 1#2F2 1#5D; a=#5B0 0 0 0 1#2F2 0 0 0 0 1#2F2 0 0 0 0 1 0 #5D; b = #5B1#2F6 1#2F3 1#2F3 1#2F6#5D; ord = 4; #5Bn, m#5D = size#28L0#29; I = eye#28n#29; for tn = t0 : h : tf-eps #25 #25 integrate the orthogonal flow #25 P1 = I; K1 = QRflow#28L0#29; U2 = h * a#282,1#29 * K1; P2 = ER_expm#28U2#29*P1; K2 = B_RK4#28P2, L0#29; #25 evaluates B#28P2*L0*P2^T#29 K2 = dexpinvr#28U2,K2,ord#29; U3 = h * #28a#283,1#29 * K1 + a#283,2#29 * K2#29; P3 = ER_expm#28U3#29*P1; K3 = B_RK4#28P3, L0#29; K3 = dexpinvr#28U3,K3,ord#29; U4 = h * #28a#284,1#29 * K1 + a#284,2#29 * K2 + a#284,3#29*K3#29; P4 = ER_expm#28U4#29*P1; K4 = B_RK4#28P4, L0#29; K4 = dexpinvr#28U4,K4,ord#29; V = h * #28b#281#29 * K1 + b#282#29 * K2 + b#283#29 * K3 + b#284#29*K4#29; Y1 = ER_expm#28V#29*P1; L1 = Y1 * L0 * Y1 apos;; #25 update the numerical solution L0 = L1; end... ..."

### Table 5: Performance of individual and combination scoring functions on six decoy sets.

"... In PAGE 10: ...ttp://www.biomedcentral.com/1472-6807/2/3 eliminated 10% of the conformations with each filter un- til we were left with one conformation. In the experiment in Table5 , we compare the average performance of each of the individual filters to our final hierarchical combina- tion when reducing the 10,000 conformations generated for each protein by our search method (corresponding to the last entry in Table 4) to 1000 conformations. The hi- erarchical combination first reduces the 10,000 confor- mations to 8000 by applying the density function, which is then reduced to 6000 by applying the hydrophobic compactness function, which is then reduced to 4000, 3000, 2000, and 1000 in the same order as presented in Table 5.... In PAGE 10: ... The hi- erarchical combination first reduces the 10,000 confor- mations to 8000 by applying the density function, which is then reduced to 6000 by applying the hydrophobic compactness function, which is then reduced to 4000, 3000, 2000, and 1000 in the same order as presented in Table 5. Table5 shows that particularly promising filters include the use of density-based scoring functions, hydrophobic compactness, all-atom pairwise preferences and match of the final conformation to the predicted secondary struc- ture. Physics-based functions based on electrostatics and van der Waals interactions do not discriminate well on their own, and only do so when an explicit solvation term is added to the functions.... In PAGE 10: ... Physics-based functions based on electrostatics and van der Waals interactions do not discriminate well on their own, and only do so when an explicit solvation term is added to the functions. Table5 also shows that even though some of the individ- ual functions perform well, the combination of all the functions applied in a hierarchical manner performs the best. As mentioned earlier, this combination was devel- oped through intuition under pressure from the CASP ex- periment (though here the goal was to reduce the total number of conformations to five).... ..."

### Table 5: Performance of individual and combination scoring functions on six decoy sets.

2002

"... In PAGE 10: ...ttp://www.biomedcentral.com/1472-6807/2/3 eliminated 10% of the conformations with each filter un- til we were left with one conformation. In the experiment in Table5 , we compare the average performance of each of the individual filters to our final hierarchical combina- tion when reducing the 10,000 conformations generated for each protein by our search method (corresponding to the last entry in Table 4) to 1000 conformations. The hi- erarchical combination first reduces the 10,000 confor- mations to 8000 by applying the density function, which is then reduced to 6000 by applying the hydrophobic compactness function, which is then reduced to 4000, 3000, 2000, and 1000 in the same order as presented in Table 5.... In PAGE 10: ... The hi- erarchical combination first reduces the 10,000 confor- mations to 8000 by applying the density function, which is then reduced to 6000 by applying the hydrophobic compactness function, which is then reduced to 4000, 3000, 2000, and 1000 in the same order as presented in Table 5. Table5 shows that particularly promising filters include the use of density-based scoring functions, hydrophobic compactness, all-atom pairwise preferences and match of the final conformation to the predicted secondary struc- ture. Physics-based functions based on electrostatics and van der Waals interactions do not discriminate well on their own, and only do so when an explicit solvation term is added to the functions.... In PAGE 10: ... Physics-based functions based on electrostatics and van der Waals interactions do not discriminate well on their own, and only do so when an explicit solvation term is added to the functions. Table5 also shows that even though some of the individ- ual functions perform well, the combination of all the functions applied in a hierarchical manner performs the best. As mentioned earlier, this combination was devel- oped through intuition under pressure from the CASP ex- periment (though here the goal was to reduce the total number of conformations to five).... ..."

### Table 1: Constructors in First-Order Description Logics

1999

"... In PAGE 3: ... The for- mer are interpreted as subsets of a given domain, and the latter as binary relations on the domain. Table1 lists constructors that allow one to build #28complex#29 concepts and roles from #28atomic#29 concept names and role names. For instance, the concept Man u9Child:#3Eu8Child:Human denotes the set of... In PAGE 3: ...Table 1: Constructors in First-Order Description Logics Description logics di#0Ber in the constructions they admit. By combining constructors taken from Table1 , two well-known hierarchies of description logics may be obtained. The logics we consider here are extensions of FL , ; this is the logic with #3E, ?, universal quanti#0Ccation, conjunction and un- quali#0Ced existential quanti#0Ccation 9R:#3E.... In PAGE 4: ... For instance, FLEU , is FL , with #28full#29 existential quanti#0Ccation and disjunction. Description logics are interpreted on interpretations I =#28#01 I ; #01 I #29, where #01 I is a non-empty domain, and #01 I is an interpretation function assigning subsets of #01 I to concept names and binary relations over #01 I to role names; complex concepts and roles are interpreted using the recipes speci#0Ced in Table1 . The semantic value of an expression E in an interpretation I is simply the set E I .... In PAGE 4: ...ome page at http:#2F#2Fdl.kr.org#2Fdl#2F. 3 De#0Cning Expressive Power In this section we de#0Cne our notion of expressive power, and explain our method for determining the expressivepower of a given description logic. Our aim in this paper is to determine the expressive power of concept expressions of every extension of FL , and AL that can be de#0Cned using the constructors in Table1 . Wesay that a logic L 1 is at least as expressive as a logic L 2 if for every concept expression in L 2 there is an equivalent concept expression in L 1 ; notation: L 2 #14 L 1 .... In PAGE 4: ... First, item 1 is next to trivial. The semantics given in Table1 induces translations #28#01#29 #1C and #28#01#29 #1B taking concepts and roles, respectively, to formulas in a #0Crst-order language whose signature consists of unary predicate symbols corresponding... In PAGE 7: ... Hence, ALC #3C ALCR, ALCN, ALCRN. a Now, what do we need to do to adapt the above result for other exten- sions of FL , de#0Cned by Table1 ? For logics less expressive than ALC we... In PAGE 8: ... We #0Crst consider the `minimal apos; logic FL , ,char- acterize its concepts semantically, and use the characterization to separate FL , from richer logics. After that, we treat each of the constructors in Table1 that are not in FL , , and examine which changes are needed to characterize the concepts de#0Cnable in the resulting logics. This is followed by a brief section in which we consider combinations of constructors.... In PAGE 18: ... FL , FLE , FLU , AL FLN , FLR , FLEU , ALE FLEN , FLER , ALU FLUN , FLUR , ALN ALR FLNR , ALC FLEUN , FLEUR , ALEN ALER FLENR , ALUN ALUR FLUNR , ALNR ALCN ALCR FLEUNR , ALENR ALUNR ALCNR Figure 2: Classifying Description Logics Several comments are in order. First, the diagram does not mention all possible combinations of the constructors listed in Table1 . The reason for... In PAGE 21: ... A second important di#0Berence between Baader apos;s work and ours lies in the type of results that have been obtained. Baader only establishes a small number of separation results, whereas we provide a complete classi#0Ccation of all languages de#0Cnable using the constructors in Table1 . More importantly, our separation results are based on semantic characterizations; this gives a deeper insightinto the properties of logics than mere separation results.... In PAGE 35: ... B.6 Classifying an Arbitrary Description Logic To obtain a characterization of an arbitrary description logic #28de#0Cned from Table1 #29, simply combine the observations listed in Sections B.... ..."

Cited by 3