### Table 2.4: Semantic mapping of a triple hF S V i to formulae in probabilistic logic, as determined by the semantic type of slot S, the category status of frame F and value V , and the semantic annotations of the triple. P (A) indicates the probability of logical sentence A, and P (A1=A2) indicates the conditional probability of A1 given that P (A2) = 1.

### Table 1. conditions on accessibility logic Conditions on Accessibility

"... In PAGE 48: ... is a CL1 formula. Table1 . Flat Propositional Contrastive Logic: Syntax 2 Propositional and rst-order Contrastive Logic 2.... In PAGE 125: ... We assume a binary relation of `accessibility apos; between labels. This relation may satisfy certain conditions, and a number of such conditions is de ned in Table1 . K and various extensions of K that can be dealt with by means of labelled tableaux require certain properties of accessibility between labels.... ..."

### Table 1. conditions on accessibility logic Conditions on Accessibility

"... In PAGE 9: ... We assume a binary relation of `accessibility apos; between labels. This relation may satisfy certain conditions, and a number of such conditions is de ned in Table1 . K and various extensions of K that can be dealt with by means of labelled tableaux require certain properties of accessibility between labels.... ..."

### TABLE II. Estimated conditional probabilities of

### Table 1: An extended logic grammar

2005

"... In PAGE 7: ...Table1... In PAGE 8: ...5. Non-terminal symbols are similar to literals in Prolog; exp-1(?x) in Table1 is an example of non-terminal symbol. Commas denote concatenation and each grammar rule ends with a full stop.... In PAGE 8: ... They specify the conditions that must be satisfied before the rule can be applied. For example, the goal member(?x, [X, Y]) in Table1 instantiates the variable ?x to either X or Y if ?x has not been instantiated, otherwise it checks whether the value of ?x is either X or Y. In another example, if the variable ?y has not been bound, the goal random(0, 1, ?y) instantiates ?y to a random floating point number between 0 and 1.... In PAGE 9: ... These derivation trees form the initial population and adaptive GBGP directly manipulates these trees to find appropriate solutions. For example, the program (* (+ X 0) (+ X 0)) can be generated by adaptive GBGP given the extended logic grammar in Table1 . Its derivation tree is depicted in Figure 1.... In PAGE 10: ... Otherwise, go to step 1. Consider two parental programs generated by the grammar in Table1 , the primary program is (/ (- Y 2.2) (- Y 2.... In PAGE 35: ... The parameters used in this experiment are summarized in Table 11. The experimental results for non-adaptive GBGP with the original grammar and the first 10 adapted grammars are summarized in Table1 22. Numbers in parentheses are the standard deviations.... In PAGE 36: ...ules to be different in various contexts (i.e. rules). Since the same non-terminal symbol at the right-hand side of different rules can have different rule-biases list, rules may have different probabilities of being used in different contexts. For example, consider the grammar rule 2 in Table1 , the probabilities of applying rules 5, 6, and 7 to expand the first non-terminal symbol exp-1(?x) are 0.... ..."

Cited by 3

### Table 2. accessibility conditions for various logics

"... In PAGE 48: ... The syntax of CL1 is presented in Table 1. I now turn to the semantic de nition of CL1, presented in Table2 . I use `j= apos; to ambiguously denote satisfaction both of a classical propositional formula over one world, and for the satisfaction of a contrastive formula over two worlds, leaving the distinction to context.... In PAGE 49: ...PROPOSITIONAL AND FIRST-ORDER CONTRASTIVE LOGIC 729 hS; Ai j= iff A j= ; for propositional (P) hS; Ai j= iff S j= : and A j= (S) hS; Ai j= iff S j= and A j= (C) hS; Ai j= ! iff S j= (W) hS; Ai j= ! iff A j= (A) hS; Ai j= iff S j= ! : and A j= ^ (B) Table2 . Flat Propositional Contrastive Logic: Semantics 4.... In PAGE 126: ... 402)), namely: L2 X; ( ; 2A) ! Y ` X; ( ; A) ! Y for any accessible from provided (i) for K; KB; and K4; must be available on the branch; (ii) for KD; KT; KDB; KTB; KD4; S4; and S5; must either be available on the branch or must be a simple, unrestricted extension of R2 X ! ( ; 2A); Y ` X ! ( ; A); Y provided is a simple, unrestricted extension of The tableau rules for _, :, 8 and the structural rules mon and cut remain unchanged. If S is any system listed in Table2 , let TQS be the tableau presentation of its constant domain rst-order extension. If we try to reuse the proof of strong cut-elimination for TQS5 in order to establish strong cut-elimination for TQS, we have to be careful, since both R2 and L2 come with complex side conditions.... ..."

### Table 2. accessibility conditions for various logics

"... In PAGE 10: ... 402)), namely: L2 X; ( ; 2A) ! Y ` X; ( ; A) ! Y for any accessible from provided (i) for K; KB; and K4; must be available on the branch; (ii) for KD; KT; KDB; KTB; KD4; S4; and S5; must either be available on the branch or must be a simple, unrestricted extension of R2 X ! ( ; 2A); Y ` X ! ( ; A); Y provided is a simple, unrestricted extension of The tableau rules for _, :, 8 and the structural rules mon and cut remain unchanged. If S is any system listed in Table2 , let TQS be the tableau presentation of its constant domain rst-order extension. If we try to reuse the proof of strong cut-elimination for TQS5 in order to establish strong cut-elimination for TQS, we have to be careful, since both R2 and L2 come with complex side conditions.... ..."

### Table 3: Conditions for State Transition from State VI.

1997

"... In PAGE 4: ...3 State Transitions and Probabilities In this section, we use the six process states intro- duced in the previous section and enumerate all valid process-state transitions. Tables 2 and 3 enumerate the probabilities #28Table 2#29 and the logical conditions that must hold #28 Table3 #29 for all valid process-state transi- tions during each round. Transitions shown with a zero probability of occurrence and those not shown are not allowable according to the protocol description and our assumed fault model.... In PAGE 5: ...In Table3 , we consider the logical conditions that must hold for process-state transitions from state VI. The #0Crst rowofTable 3 shows that one possibilityisfor this process to crash #28state I#29, with probability p crash .... In PAGE 5: ...In Table 3, we consider the logical conditions that must hold for process-state transitions from state VI. The #0Crst rowof Table3 shows that one possibilityisfor this process to crash #28state I#29, with probability p crash . If it does not crash, it might receive a message #28valid- valued, null-valued or #5CI don apos;t know quot;#29 from one of the other processes.... In PAGE 5: ... We now derive the transition probabilities of process-state transitions from state VI. The logical ex- pressions presented in Table3 hold true independentof the distribution assumed for process failure and mes- sage transmission times. However, the probabilities assigned to these events depend on the process fail- ure and message delay distributions.... In PAGE 5: ... This requires the common mean #28S#29 of each of the #18 exponential stages that comprise the Erlang, to be S =#28M=#18#29. The following expression gives the value of P#5BT #14 R#5D in the Erlangian case: P#5BT #14 R#5D Erlangian =1, e , R S #28 #18,1 X i=0 #28 R S #29 i i! #29: We observe from Table3 that all the logical condi- tions pertaining to message transmissions have one of the following two forms: a speci#0Ced process receives at least one of the Num i... ..."

Cited by 5

### 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. Conditional probabilities of realizations.

"... In PAGE 9: ... This implies that n0e n3d1n3dNn2c so the exn2dante probability for each project to belong to U f e n12 g is inn0cnitesimal. Table1 summarizes the conditional probabilities of the din0berent realizations for each project. Table 1.... In PAGE 10: ... Table1 . The n0crst is the one discussed in the above paragraphn3a as the number of projects increasesn2c the information about the underlying state of nature improves.... In PAGE 18: ... We can think of choosing low en0bort in this setting as experimentation because it has a lower direct return than high en0bort but it has the potential of revealing socially useful information. This feature is considerably more general than our formalizationn3a for instancen2c consider a more complex matrix of actions and payon0bs than Table1 n3a some actions would require high en0bortn2c and a subset of these would havelower private return but reveal more information. The actions that reveal more information would play the same role as low en0bort in our example.... ..."