We analyze the logical form of the domain knowledge that grounds analogical inferences and generalizations from a single instance. The form of the assumptions which justify analogies is given schematically as the "determination rule", so called because it expresses the relation of one set of variables determining the values of another set. The determination relation is a logical generalization of the different types of dependency relations defined in database theory. Specifically, we define determination as a relation between schemata of first (...) order logic that have two kinds of free variables: (1) object variables and (2) what we call "polar" variables, which hold the place of truth values. Determination rules facilitate sound rule inference and valid conclusions projected by analogy from single instances, without implying what the conclusion should be prior to an inspection of the instance. They also provide a way to specify what information is sufficiently relevant to decide a question, prior to knowledge of the answer to the question. (shrink)

Selection type theories solve adaptation problems. Natural selection, clonal selection for antibody production, and selective theories of higher brain function are examples. An abstract characterization of typical selection processes is generated by analyzing and extending previous work on the nature of natural selection. Once constructed, this abstraction provides a useful tool for analyzing the nature of other selection theories and may be of use in new instances of theory construction. This suggests the potential fruitfulness of research to find other theory (...) types and construct their abstractions. (shrink)

Confronted with problems or situations that do not yield toknown theories and world views, scientists and students are alike. Theyare rarely able to directly build a model or a theory thereof. Rather,they must find ways to make sense of the circumstances using theircurrent knowledge and adjusting what is recognized in the process. Thisway of thinking, using past ways of perceiving the physical world tobuild new ones does not follow a logical path and cannot be described astheory revision. Likewise, in many (...) situations it is awkward, indeedoften impossible, to resort to analogical reasoning to account for it.This paper presents a new mechanism, called `tunnel effect', that mayexplain, in part, how scientists and students reason while constructinga new conceptual domain. `Tunnel effect' is also contrasted withanalogical reasoning. (shrink)