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We describe an approach to the inductive synthesis of recursive equations from input/outputexamples which is based on the classical two-step approach to induction of functional Lisp programs of Summers (1977). In a first step, I/O-examples are rewritten to traces which explain the outputs given the respective inputs based on a datatype theory. This traces(More)
We present an approach to folding of finite program terms based on the detection of recurrence relations in a single given term which is considered as the kth unfolding of an unknown recursive program. Our approach goes beyond Summers’ classical approach in several aspects: It is language independent and works for terms belonging to an arbitrary term(More)
We present an approach to analogical reasoning which is inherently dependent on abstraction. While typical cognitive and AI models of analogy perform a direct mapping from objects of the base to objects of the target domain, our model performs mapping via abstraction. Abstraction is calculated as most specific generalization of the base and the target(More)
We present an approach to spatial reasoning that is based on homogenous coordinate systems and their transformations. In contrast to qualitative approaches, spatial relations are not represented by symbolic expressions only but additionally by parameters with constraints, which are subsets of real numbers. Our work is based on the notion of mental models in(More)
In this paper we present a comparison of several inductive programming (IP) systems. IP addresses the problem of learning (recursive) programs from incomplete specifications, such as input/output examples. First, we introduce conditional higher-order term rewriting as a common framework for inductive logic and inductive functional program synthesis. Then we(More)
We propose to characterize structural similarity between source and target problems by the type and size of their structural overlap. Size of structural overlap is captured by a measure of graph-distance. We investigated the influence of structural overlap on transfer success in analogical problem solving in two experiments. In both experiments, for a fixed(More)
In this paper we present an approach to the induction of re-cursive structures from examples which is based on the notion of recursive program schemes. We separate induction from examples in two stages: (1) constructing initial programs from examples and (2) folding initial programs to recursive program schemes. By this separation, the induction of(More)