### Table 1: Queries for various states of learnability.

"... In PAGE 6: ...1 Concept Isolation Evaluation We evaluated the precision performance for concepts be- longing to one of the four possible learnability states de- picted in Figure 5. The representative concepts we queried, based on their learnability states, are shown in Table1 . The angle diversity (AD) sampling strategy is used as the base- line for comparing the performance of the other algorithms used to modify the sample pool, namely disambiguate input- space (DS) and disambiguate keywords (DK).... ..."

### Table 1: Queries for various states of learnability.

in Abstract

"... In PAGE 29: ... We evaluated retrieval accuracy (in terms of precision) for concepts belonging to one of the four possible learnability states depicted in Figure 11. The representative concepts we queried, based on their learnability states, are shown in Table1 . The angle diversity (AD) sampling strategy is used as the baseline for comparing the performance of the other algorithms used to modify the sample pool, namely disambiguate input-space (DS) and disambiguate keywords (DK).... ..."

### Table 1: A summary of the learnability results

1995

"... In PAGE 28: ...ase case. This was our strongest positive result. These results are summarized in Tables 1 and 2. In Table1 , a program with one r- ary recursive clause is denoted rC R , a program with one r-ary recursive clause and one nonrecursive basecase is denoted rC R ;C B ,orrC R jC B if there is a #5Cbasecase quot; oracle, and a program with s di#0Berent r-ary recursive clauses is denoted s #02 rC R . The boxed results are associated with one or more theorems from this paper, or its companion paper, and the unmarked results are corollaries of other results.... In PAGE 28: ... A #5C+ quot; after a program class indicates that it is identi#0Cable from equivalence queries; thus the positive results described above are summarized by the four #5C+ quot; entries in the lower left-hand corner of the section of the table concerned with constant-depth determinate clauses. Table 2 presents the same information in a slightly di#0Berent format, and also relates the notation of Table1 to the terminology used elsewhere in the paper. This paper has considered the learnability of the various natural generalizations of the languages shown to be learnable in the companion paper.... In PAGE 29: ...then this language is not learnable: even a single linear recursive clause is not polynomially predictable. Again, these results are summarized in Table1 ; a #5C, quot; after a program class means that it is not polynomially predictable, under cryptographic assumptions, and hence neither pac-learnable nor identi#0Cable from equivalence queries. The negative results based on cryptographic hardness give an upper bound on the ex- pressiveness of learnable recursive languages, but still leave open the learnability of programs with a constantnumber of k-ary recursive clauses in the absence of a basecase oracle.... In PAGE 29: ... These results suggest, therefore, that pac-learning multi-clause recursive logic programs is di#0Ecult; at the very least, they show that #0Cnding a provably correct pac-learning algorithm will require substantial advances in computational learning theory.In Table1 , a #5C= Dnf quot; #28respectively #15 Dnf#29 means that the corresponding language is prediction-equivalent to DNF #28respectively at least as hard as DNF#29. To further summarize Table 1: with any sort of recursion, only programs containing constant-depth determinate clauses are learnable.... In PAGE 29: ...InTable 1, a #5C= Dnf quot; #28respectively #15 Dnf#29 means that the corresponding language is prediction-equivalent to DNF #28respectively at least as hard as DNF#29. To further summarize Table1 : with any sort of recursion, only programs containing constant-depth determinate clauses are learnable. The only constant-depth determinate recursive programs that are learnable are those that contain a single k-ary recursive clause #28in the standard equivalence query model#29 or a single k-ary recursive clause plus a base case #28if a #5Cbasecase oracle quot; is allowed#29.... ..."

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### Table 2: Summary by language of the learnability results. Column B indicates the number

1995

"... In PAGE 28: ... A #5C+ quot; after a program class indicates that it is identi#0Cable from equivalence queries; thus the positive results described above are summarized by the four #5C+ quot; entries in the lower left-hand corner of the section of the table concerned with constant-depth determinate clauses. Table2 presents the same information in a slightly di#0Berent format, and also relates the notation of Table 1 to the terminology used elsewhere in the paper. This paper has considered the learnability of the various natural generalizations of the languages shown to be learnable in the companion paper.... ..."

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### Table 1: Summary of our results for acyclic circuits Depth Fan-in Gates Query types Learnability Reference

2006

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### Table 1: Summary of our results for acyclic circuits Depth Fan-in Gates Query types Learnability Reference

2005

### Table 1: Summary of our results Depth Fan-in Gates Query types Learnability Reference

### Table 2: Comparison of the Models on Arbitrary Boolean and Purely Conjunctive Queries. Conjunctive Arbitrary

2000

"... In PAGE 12: ... The only di erence is that the connective between two attributes was selected as either a disjunction or a conjunction by ipping a fair coin. Table2 compares results on arbitrary and purely conjunctive queries (nQ is the query length, tP , Ct and eP are the average online time, query count and error across 200 runs of the algorithms). The maxent models again enjoy a distinct advantage in accuracy over the independence models.... ..."

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### Table 2: Semantics of n-ary Conjunctive Queries

2006

"... In PAGE 3: ... Query semantics. Let D be the data graph the query Q is evaluated over and q the number of variables occurring in Q, then Table2 gives the precise semantics of n-ary conjunctive queries over graphs as used in this article. The semantics is defined based on sets of valuations for query variables.... ..."

Cited by 1

### Table 3. A nondeterministic algorithm for deciding conjunctive queries in EL++.

2007

"... In PAGE 7: ...entation for role paths (e.g. by guessing a single path), but our formulation reduces nondeterminism and eventually simplifies our investigation of algorithmic complexity. Our algorithm for deciding conjunctive query entailment is given in Table3 . Any occurrence of the word select in the description indicates a nondeterministic choice of the algorithm.... In PAGE 12: ... Proof. First consider Step A of Table3 . It clearly can be performed nondeterministi- cally in polynomial time.... ..."

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