### Table 1 Complexity results of abduction from default theories.

2002

"... In PAGE 5: ... 2 Abstracting from the particular kind of expla- nation, the main decision problems in the context of abductive reasoning are the following: consistency: Does a given nite default abduc- tion problem possess an explanation? relevance: Given some nite default abduction problem P = hH; M; W; i and a set H0 H, is H0 relevant for P? necessity: Given some nite default abduction problem P = hH; M; W; i and a set H0 H, is H0 necessary for P? Concerning the computational complexity of these tasks, as shown in [12], these problems are located between the second and fourth level of the polynomial hierarchy. Table1 gives the speci c results; each entry C represents completeness of the corresponding problem for the class C.1 As can be seen from these results, skeptical abduction is always one level harder than brave abduction.... ..."

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### Table 4: Abduction on circuits: ZBDD-based LV -BE.

"... In PAGE 5: ... This problem can be addressed through LV -BE with V = I [ O. In this case, the trie-based implementation failed in all bench- marks (except adder-5), so we only report results for the ZBDD-based implementation, in Table4 . We also tried our algorithms on the ISCAS circuits benchmark family, without success.... ..."

### Table 8: Ratio of adversarial time to total running time for the budgets model

2005

"... In PAGE 26: ...00 2.00 Table 7: Performance statistics { integral budgets In Table8 we compare the time spent solving adversarial problems to the total running time of our algorithm. Each problem category shows an average over 100 sample runs.... ..."

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### Table 3. Sketch of a possible representation of the mapping pl of an HD- independent abductive problem.

### Table 2.1: Solving the adversarial problem as a mixed-integer program

2006

### Table 1. How the adversarial and incremental constraints contribute to the perfor- mance of the problems discussed in Section 3.

### Table 4 Software geospatial agents

"... In PAGE 10: ... For example, an agent-based system may retrieve geospatial information for the user from a distributed data repository and then carry out multiple tasks related to data mining and knowledge discovery, data fusion, geocompu- tation resources monitoring, and semantic interoperability. Table4 summarizes the various researchers working on developing agents for GIScience applications. Each instance provides a brief description and categorizes applications... ..."

### Table 4: Abduction on circuits: ZBDD-based C4CE -BE.

2001

"... In PAGE 5: ... This problem can be addressed through C4CE -BE with CE BP C1 CJ C7. In this case, the trie-based implementation failed in all bench- marks (except adder-5), so we only report results for the ZBDD-based implementation, in Table4 . We also tried our algorithms on the ISCAS circuits benchmark family, without success.... ..."

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