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In the present paper we propose a consistent way to integrate syntactical least general generalizations (lgg's) with semantic evaluation of the hypotheses. For this purpose we use two different relations on the hypothesis space - a constructive one, used to generate lgg's and a semantic one giving the coverage-based evaluation of the lgg. These two relations jointly implement a semantic distance measure. The formal background for this is a height-based definition of a semi-distance in a join semi-lattice. We use some basic results from lattice theory and introduce a family of language independent coverage-based height functions. The theoretical results are illustrated by examples of solving some basic inductive learning tasks.

Metric-Based Inductive Learning Using Semantic Height Functions