this article we outline the foundations of such a theory, working in the general framework of Bayesian inference. Much of our proposal for extending Shepard's theory to the cases of multiple examples and arbitrary stimulus structures has already been introduced in other papers (Griffiths & Tenenbaum, 2000; Tenenbaum, 1997, 1999a, 1999b; Tenenbaum & Xu, 2000). Our goal here is to make explicit the link to Shepard's work and to use our framework to make connections between his work and other models of learning (Feldman, 1997; Gluck & Shanks, 1994; Haussler, Kearns & Schapire, 1994; Kruschke, 1992; Mitchell, 1997), generalization (Nosofsky, 1986; Heit, 1998), and similarity (Chater & Hahn, 1997; Medin, Goldstone & Gentner, 1993; Tversky, 1977). In particular, we will have a lot to say about how our generalization of Shepard's theory relates to Tversky's (1977) well-known set-theoretic models of similarity. Tversky's set-theoretic approach and Shepard's metric space approach are often considered the two classic -- and classically opposed -- theories of similarity and generalization. By demonstrating close parallels between Tversky's approach and our Bayesian generalization of Shepard's approach, we hope to go some way towards unifying these two theoretical approaches and advancing the explanatory power of each. The plan of our article is as follows. In Section 2, we recast Shepard's analysis of generalization in a more general Bayesian framework, preserving the basic principles of his approach in a form that allows us to apply the theory to situations with multiple examples and arbitrary (non-spatially represented) stimulus structures. Sections 3 and 4 describe those extensions, and Section 5 concludes by discussing some implications of our theory for the internalization of...

Abstract. An innate characteristic of the development of ontologies is that they are often created by independent groups of expertise, which generates the necessity of merging and aligning ontologies covering overlapping domains. However, a central issue in the merging process is the evaluation of the differences between two ontologies, viz. the establishment of a similarity measure between their concepts. Many algorithms and tools have been proposed for merging of ontologies, but the majority of them disregard the structural properties of the source ontologies, focusing mostly on syntactic analysis. This article focuses on the alignment of ontologies through Formal Concept Analysis, a data analysis technique founded on lattice theory, and on the use of similarity measures to identify cross-ontology related concepts. 1