# Catalogue of Artificial Intelligence Techniques

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## Meta-level Inference

### Categories: Inference and Reasoning , Theorem Proving

Author(s): **Fausto Giunchiglia, Frank van Harmelen, Robin Boswell**

The word `Meta-X' can be read as `X about X'. So, for instance the word `Meta-knowledge' can be read as `knowledge about knowledge', the word `meta-level' as `at a level about another level' and the word `meta-level inference as `inference performed at a level which is about another level'. More generally, when speaking of meta-level inference, we think of the following:

- There are two theories, one (usually called the
*object theory*) which is about a given topic, and another one (usually called the*meta-theory*) which is about the object theory. The two theories may or may not in general share the same language. - The inferences performed in the meta-theory are called `meta-level inferences'. In general, the process of carrying on deduction in the meta-theory is called `meta-level inference'.

- ${x}_{}^{2}-3x+2=0\text{}\to \text{}x=1\text{or}2$ .
- ${x}_{}^{2}-3x+2=0\text{}$ contains two occurrences of the unknown `$x$ '.

*better results*about the topic of interest. Better results can mean `to solve the problem in less time' (in which case the meta-level inference is used to control or guide the search at the object level), `to get results otherwise unavailable' (in which case the meta-level inference is used to extend the solutions possibly obtainable by the object level) or `to describe the object-level' (in which case the meta-level inference is used to get a better understanding on the object level which can then be used for further operations, e.g., learning), and so on.

### References:

- Aiello, L. and Levi, G.,
*The uses of metaknowledge in AI sytems*Proceedings of ECAI-84 (1984), 705--717.

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