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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'.

For instance,

.
contains two occurrences of the unknown ` '.

are statements in respectively the theory and the meta-theory of algebra. The goal of object-level inference is to obtain results in the topic of interest. The goal of meta-level inference is to obtain results about the theory of the topic of interest (the object theory) and then to use them to obtain 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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