In this paper, I argue that it is typical of many scientific reasoning processes that they involve the integrated use of inductive and deductive steps. I moreover illustrate with examples from the sciences that the distinction between induction and deduction is context-dependent— an inference treated in one context as deductive may in a different context may be treated as inductive—and that the...

Inductive Inference Machines (IIMs) attempt to identify functions given only input-output pairs of the functions. Pro6a6ilistic IIMs are defined, as is the probability that a probabilistic IIM identifies a function with respect to two common identification criteria: EX and BC. Let ID denote either of these criteria. Then IDpm&) is the family of sets of functions U for which there is a probabili...

Every locally complete inductive limit of sequentially complete locally convex spaces , which satisfies Retakh's condition (M) is regular, sequentially complete and sequentially retractive. A quasiconverse for this theorem and a criterion for sequential retractivity of inductive limits of webbed spaces are given.

We consider the problem of quickest change-point detection in data streams. Classical change-point detection procedures, such as CUSUM, Shiryaev-Roberts and Posterior Probability statistics, are optimal only if the change-point model is known, which is an unrealistic assumption in typical applied problems. Instead we propose a new method for change-point detection based on Inductive Conformal M...

Science and mathematics seem to be huge success stories. Hence it is not surprising that most scientists and mathematicians think that science and mathematics are the most secure ways of acquiring knowledge, and that all knowledge could, at least in principle, be derived using either the scientific method, using inductive reasoning, and in the case of mathematical knowledge, using deductive rea...

The aim of this research is to develop a strat­ egy of reasoning under uncertainty in the context of the Fuzzy Inductive Reasoning methodology. This methodology allows the prediction of systems behavior by means of two different schemes. The first one corre­ sponds to a pattern prediction scheme, based exclusively on pattern rules. The second one corresponds to a purely Sugeno infer­ ence syste...

In this position paper, we give a critical analysis of the deductive and inductive approaches to program synthesis, and of the current research in these fields. From the shortcomings of these approaches and works, we identify future research directions for these fields, as well as a need for cooperation and cross-fertilization between them.

This paper demonstrates that generating arguments in natural language requires planning at an abstract level, and that the appropriate abstraction cannot be captured by approaches based solely upon coherence relations. An abstraction based planning system is presented which employs operators motivated by empirical study and rhetorical maxims. These operators include a subset of traditional dedu...

This position paper presents a framework for inductive machine learning which includes higher-order concepts and is su ciently general to include most of the extant (symbolic) inductive learning frameworks and systems.