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An Inductive Reasoning Task is a reasoning task that requires an inductive argument (based on inductive operations on facts/evidence).

## References

### 2018a

• (Wikipedia, 2018) ⇒ https://en.wikipedia.org/wiki/Inductive_reasoning Retrieved:2018-6-24.
• Inductive reasoning (as opposed to deductive reasoning or abductive reasoning) is a method of reasoning in which the premises are viewed as supplying some evidence for the truth of the conclusion. While the conclusion of a deductive argument is certain, the truth of the conclusion of an inductive argument may be probable, based upon the evidence given. Many dictionaries define inductive reasoning as the derivation of general principles from specific observations, though some sources disagree with this usage.

The philosophical definition of inductive reasoning is more nuanced than simple progression from particular/individual instances to broader generalizations. Rather, the premises of an inductive logical argument indicate some degree of support (inductive probability) for the conclusion but do not entail it; that is, they suggest

truth but do not ensure it. In this manner, there is the possibility of moving from general statements to individual instances (for example, statistical syllogisms, discussed below).

### 2009a

• WordNet
• generalization: reasoning from detailed facts to general principles

### 2009f

• http://clopinet.com/isabelle/Projects/ETH/Exam_Questions.html
• Inference refers to the ability of a learning system, namely going from the "particular" (the examples) to the "general" (the predictive model). In the best of all worlds, we would not need to worry about model selection. Inference would be performed in a single step: we input training examples into a big black box containing all models, hyper-parameters, and parameters; outcomes the best possible trained model. In practice, we often use 2 levels of inference: we split the training data into a training set and a validation set. The training set serves the trains at the lower level (adjust the parameters of each model); the validation set serves to train at the higher level (select the model.) Nothing prevents us for using more than 2 levels. However, the price to pay will be to get smaller data sets to train with at each level.

### 2008

• Vladimir N. Vapnik. (2000). “COLT interview. http://www.learningtheory.org/index.php?view=article&id=9
• My current research interest is to develop advanced models of empirical inference. I think that the problem of machine learning is not just a technical problem. It is a general problem of philosophy of empirical inference. One of the ways for inference is induction. The main philosophy of inference developed in the past strongly connected the empirical inference to the inductive learning process. I believe that induction is a rather restrictive model of learning and I am trying to develop more advanced models. First, I am trying to develop non-inductive methods of inference, such as transductive inference, selective inference, and many other options. Second, I am trying to introduce non-classical ways of inference.

### 2000a

In abduction, H is generally restricted to a set of atomic ground or existentially quantified formulae (called assumptions) and B is generally quite large relative to H. On the other hand, in induction, H generally consists of universally quantified Horn clauses (called a theory or knowledge base), and B is relatively small and may even be empty. In both cases, following Occam's Razor, it is preferred that H be kept as small and simple as possible.