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Committed toProf. Dr. Dr.h.c. Herbert Zeitler at the party of his eightieth birthdayProf. Dr. Dr.h.c. Helmut Karzel at the social gathering of his seventy fifth birthdayProf. Dr. Dr.h.c Grozio Stanilov at the social gathering of his seventieth birthdayVarna (Bulgaria), September 5-10, 2003

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In this language, we show that monomials are PAC-learnable and then efficient algorithms exist. We give the proof for completeness as we work with the multi-table representation and that we do not have the same parameters as Cohen and Following, [3], this concept language is noted Theorem 1. For any fixed learnable. the language family is PAC- Proof 1. We use the proof technique given by [46] (lemma 1): we reduce learning in to learning monomials in a boolean space, which is known to be PAC-learnable.

DJANGO only solves the existence question and does not give all substitutions, but as discussed above this is sufficient for certain applications coming from the standard ILP setting. We have integrated the DJANGO code, generously provided by Jérome Maloberti, as a module in our system. 2 Discretization The system includes a capability for handling numerical data by means of discretization. Several approaches to discretization have been proposed in the lit- 34 M. Arias and R. Khardon erature [10,9,2].

Adj(l,0)]When considering the “relevant background mode”, we include in the examples instantiations of lt and adj whose arguments appear in the position atom directly: [position(7, 6, 5, 0, 4, 1), lt(4,5),lt(4,7),lt(5,7),adj(4,5),adj(5,4), lt(0,1),lt(0,6),lt(1,6),adj(0,1),adj(1,0)]Table 1 includes results of running our system in both modes. We trained LOGAN-H on samples with various sizes chosen randomly among the 10000 available. We report accuracies that result from averaging among 10 runs over an independent test set of 10000 examples.

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6th International conference on geometry and applications

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