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P. Geibel and F. Wysotzki. A logical framework for graph theoretic decision tree learning. In N. Lavrac and S. Dzeroski, editors, Proc. ILP 97. Springer, 1997.

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Peter Geibel and Fritz Wysotzki. A logical framework for graph theoretic decision tree learning. In N. Lavrac and S. Dzeroski, editors, Proceedings ILP 97. Springer-Verlag, 1997.

....ers for states and transitions. As already stated above, we assume to have complete predicate logic descriptions of the states where only positive literals are indicated. In the example tree of gure 2.2 for some states the description is indicated. The classi cation is performed by subsumption (Geibel and Wysotzki 1997), i.e. matching of transitions and states respectively by templates with alphabethical (unique) substitutions of the variables in the templates by constants, i.e. individual objects from the domain. In the following, two examples for template matching are given. The classi cation by (1) 4) ....

Geibel, P. and F. Wysotzki (1997). A logical framework for graph theoretic decision tree learning. In N. Lavrac and s. Dzeroski (Eds.), Procs. of the International Workshop on Inductive Logic Programming (ILP '97), Volume 1297 of LNAI, S. 166-173. Springer Verlag Berlin.

....variable bindings are enforced to be injective. Each clause is terminated with a cut. This way the learned program constitutes a decision list. The system is based on a least generalization algorithm (ff generalization) which enforces the condition of injectiveness on the variables (see [3, 2]) The least ff generalizations are constructed from 1 Plotkin s least generalization (lgg) To reduce the exponential cost caused by the complexity of the employed clique search, a modified variant of the MAXCLIQUE algorithm of Carraghan and Pardalos is used. The system is prototypical for a ....

....symbols, and a sorted variable binding fi. For definite clauses it suffices to consider Herbrand interpretations where each term is interpreted by itself. A Herbrand model can be represented by a subset of the the Herbrand base that contains all ground (variable free) atoms of the language. As in [3], for learning a n ary relational concept, a training set E = fE i j 1 i eg is given, that contains e 0 definite clauses E i = class(x i 1 ; x i n ; c i ) a i 1 ; a i m i from a function free and sorted logical language ( 6] In each example E i , the body a i 1 ....

Peter Geibel. A logical framework for graph theoretic decision tree learning. Proc. ILP-97, to appear, 1997.

....that have to be defined in an appropriate way. Such definitions can be obtained by psychological experiments. The analysis of the psychological data can be done using classical statistical approaches, or alternatively with algorithms from the field of machine learning as the system TRITOP ([9, 8]) that is described in this article. In this paper, we will investigate the question, how the definitions of spatial relations can be learned from a given set or series of example configurations (mental models) for the relation in questions. This means that the constraints have to be inferred ....

....Because the number of such objects cannot be determined in advance, a feature vector does not suffice to describe the scene, i.e. a relational description that is able to represented an unrestricted number of objects has to be used. In this paper, we will use the graph based learning system TRITOP [9, 8] for the inference task. In contrast to most ILP learning systems it relies on ideas from graph theory and is therefore especially well suited for the learning problem at hand. It has an expressive hypothesis language and incorporates a variety of standard learning techniques as generalization and ....

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Peter Geibel and Fritz Wysotzki. A logical framework for graph theoretic decision tree learning. In N. Lavrac and S. Dzeroski, editors, Proceedings ILP 97. Springer-Verlag, 1997.

.... that in this domain clearly outperform their propositional counterparts ( 9] Though most relational learning systems belong to the field of ILP (Inductive Logic Programming, e.g. 6] graph theoretical learning systems have proved to be at least as well suited for practical learning tasks ([4, 5]) NO2 biphenyl NO2 NO2 Figure 2 reduction with information loss (pattern biphenyl) If the training set consists of relational structures represented by graphs, the relational equivalent of association rules has to comprise the items occuring together and the relations between the items ( 2] ....

....one seven one C C C C seven seven seven seven seven C H type3 type22 C type3, H one C two two one C one seven one seven seven seven one C one C Figure 7 reducing ability 0. 59 For our experiments with SGM we used a transformed version of the dataset that can be used by the learning system TRITOP [5]. For example, the substance d191 containing the literals atm(d191, d191 1, c, 22, 0.133) atm(d191, d191 2, c, 22, 0.133) bond(d191, d191 1, d191 2, 7) and bond(d191, d191 2, d191 3, 7) is characterized by the transformed example clause class(inactive) charge(D191 1, 0.133) type22(D191 ....

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P. Geibel and F. Wysotzki. A logical framework for graph theoretic decision tree learning. In N. Lavrac and S. Dzeroski, editors, Proc. ILP 97. Springer-Verlag, 1997.

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