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Generalizing the Standard Format

Chapter
Part of the Trends in Logic book series (TREN, volume 38)

Abstract

In this chapter we generalize the standard format of adaptive logics and thereby introduce an interesting larger class of adaptive logics that can be characterized in a simple and intuitive way. We demonstrate that the new format overcomes the two shortcomings of the standard format. On the one hand, logics with both qualitative and quantitative rationales can be expressed in it. On the other hand, the format is expressive enough to allow for the handling of priorities in various ways. We show that many adaptive logics that have been considered in the literature fall within this larger class -for instance adaptive logics in the standard format, adaptive logics with counting strategies, lexicographic adaptive logics-and that the characterization of this class offers many possibilities to formulate new logics. One of the advantages of the format studied in this chapter is that a lot of meta-theory comes for free for any logic formulated in it. We show that adaptive logics formulated in it are always sound and complete. Furthermore, many of the meta-theoretic properties that are usually associated with the standard format (such as cumulativity, fixed point property, (strong) reassurance, etc.) also hold for rich subclasses of logics formulated in the new format.

Notes

Acknowledgments

The results presented in this chapter are the product of joint research with Frederik Van De Putte.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.GhentBelgium

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