Abstract
In the field of deductive logic, relevant logic has been investigated for a long time, as a means to derive only conclusions which are related to all premises. Our proposal is to apply this concept of relevance as a criterion of appropriateness to hypotheses in inductive logic, and in this paper we present some special hypotheses called residue hypotheses, which satisfy such kind of appropriateness. This concept of relevance is different from those often introduced in the field of Inductive Logic Programming. While those aimed at the reduction of search spaces, which went hand in hand with postulating criteria which restricted the appropriateness of formulae as hypotheses, the relevance concept presented in this paper can be regarded as ‘logical smallness’ of hypotheses, in contrast to ‘syntactical smallness’. We also give a further refinement, so-called minimized residue hypotheses, which constitute an interesting trade-o. between these two types of smallness. We also give some results on bottom clauses and relevance.
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Fronhöfer, B., Yamamoto, A. (2002). Minimised Residue Hypotheses in Relevant Logic. In: Cesa-Bianchi, N., Numao, M., Reischuk, R. (eds) Algorithmic Learning Theory. ALT 2002. Lecture Notes in Computer Science(), vol 2533. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36169-3_23
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DOI: https://doi.org/10.1007/3-540-36169-3_23
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