The context for this paper is Feferman's theory of explicit mathematics, T 0. We address a problem that was posed in F 82]. Let MID be the principle stating that any monotone operation on classiications has a least xed point. The main objective of this paper is to show that T 0 + MID, when based on classical logic, also proves the existence of non-monotone inductive deenitions that arise from a...

Inductive discovery can be said to proceed through the accumulation of evidence in attempts to refute the current theory. Typically, this has involved a straight choice between the falsi cation of a theory and its continued use, with little or no consideration given to the possibility of error. This paper addresses the problems of error and evidence evaluation. It considers a variety of di eren...

In formal approaches to inductive learning, the ability to learn is understood as the ability to single out a correct hypothesis from a range of possibilities. Although most of the existing research focuses on the characteristics of the learner, in many paradigms the significance of the teacher’s abilities and strategies is in fact undeniable. Motivated by this observation, in this paper we hig...

The notion of an inductive inference machine aggregating a team of inference machines models the problem of making use of several explanations for a single phenomenon. This article investigates the amount of information necessary for a successful aggregation of the theories given by a team of inference machines. Variations of using different kinds of identitication and aggregation are investiga...

TIP is a toolbox for users and developers of inductive provers. It consists of a large number of tools which can, for example, simplify an inductive problem, monomorphise it or find counterexamples to it. We are using TIP to help maintain a set of benchmarks for inductive theorem provers, where its main job is to encode aspects of the problem that are not natively supported by the respective pr...

Four experiments explored the effect of diversity of contrasting negative evidence on inductive inferences drawn from a single-item target. In Experiments 1 and 2, we found that increasing the diversity of a contrast set led people to infer that a target exemplar corresponded to a higher level category and led to greater generalization of a novel property associated with the target. Further, we...

We lay down plans to study how Inductive Reasoning Ability (IRA) affects the analyzing and understanding of Program Visualization (PV) systems. Current PV systems do not take into account the abilities of the user but show always the same visualization independently of the changing knowledge or abilities of the student. Thus, we propose IRA as an important skill when comprehending animation, wh...