Comparison and Mapping Facilitate Relation Discovery and Predication

Relational concepts play a central role in human perception and cognition, but little is known about how they are acquired. For example, how do we come to understand that physical force is a higher-order multiplicative relation between mass and acceleration, or that two circles are the same-shape in the same way that two squares are? A recent model of relational learning, DORA (Discovery of Relations by Analogy; Doumas, Hummel & Sandhofer, 2008), predicts that comparison and analogical mapping play a central role in the discovery and predication of novel higher-order relations. We report two experiments testing and confirming this prediction

When almost is not even close: Remarks on the approximability of HDTP

A growing number of researchers in Cognitive Science advocate the thesis that human cognitive capacities are constrained by computational tractability. If right, this thesis also can be expected to have far-reaching consequences for work in Artificial General Intelligence: Models and systems considered as basis for the development of general cognitive architectures with human-like performance would also have to comply with tractability constraints, making in-depth complexity theoretic analysis a necessary and important part of the standard research and development cycle already from a rather early stage. In this paper we present an application case study for such an analysis based on results from a parametrized complexity and approximation theoretic analysis of the Heuristic Driven Theory Projection (HDTP) analogy-making framework

Individual differences in relational learning and analogical reasoning:A computational model of longitudinal change

Children’s cognitive control and knowledge at school entry predict growth rates in analogical reasoning skill over time; however, the mechanisms by which these factors interact and impact learning are unclear. We propose that inhibitory control (IC) is critical for developing both the relational representations necessary to reason and the ability to use these representations in complex problem solving. We evaluate this hypothesis using computational simulations in a model of analogical thinking, Discovery of Relations by Analogy/Learning and Inference with Schemas and Analogy (DORA/LISA; Doumas et al., 2008). Longitudinal data from children who solved geometric analogy problems repeatedly over 6 months show three distinct learning trajectories though all gained somewhat: analogical reasoners throughout, non-analogical reasoners throughout, and transitional – those who start non-analogical and grew to be analogical. Varying the base level of top-down lateral inhibition in DORA affected the model’s ability to learn relational representations, which, in conjunction with inhibition levels used in LISA during reasoning, simulated accuracy rates and error types seen in the three different learning trajectories. These simulations suggest that IC may not only impact reasoning ability but may also shape the ability to acquire relational knowledge given reasoning opportunities

From Analogical Proportion to Logical Proportions

International audienceGiven a 4-tuple of Boolean variables (a, b, c, d), logical proportions are modeled by a pair of equivalences relating similarity indicators ( a∧b and a¯∧b¯), or dissimilarity indicators ( a∧b¯ and a¯∧b) pertaining to the pair (a, b), to the ones associated with the pair (c, d). There are 120 semantically distinct logical proportions. One of them models the analogical proportion which corresponds to a statement of the form “a is to b as c is to d”. The paper inventories the whole set of logical proportions by dividing it into five subfamilies according to what they express, and then identifies the proportions that satisfy noticeable properties such as full identity (the pair of equivalences defining the proportion hold as true for the 4-tuple (a, a, a, a)), symmetry (if the proportion holds for (a, b, c, d), it also holds for (c, d, a, b)), or code independency (if the proportion holds for (a, b, c, d), it also holds for their negations (a¯,b¯,c¯,d¯)). It appears that only four proportions (including analogical proportion) are homogeneous in the sense that they use only one type of indicator (either similarity or dissimilarity) in their definition. Due to their specific patterns, they have a particular cognitive appeal, and as such are studied in greater details. Finally, the paper provides a discussion of the other existing works on analogical proportions