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Quantitative Logic Reasoning

  • Marcelo Finger
Chapter
Part of the Trends in Logic book series (TREN, volume 47)

Abstract

In this paper we show several similarities among logic systems that deal simultaneously with deductive and quantitative inference. We claim it is appropriate to call the tasks those systems perform as Quantitative Logic Reasoning. Analogous properties hold throughout that class, for whose members there exists a set of linear algebraic techniques applicable in the study of satisfiability decision problems. In this presentation, we consider as Quantitative Logic Reasoning the tasks performed by propositional Probabilistic Logic; first-order logic with counting quantifiers over a fragment containing unary and limited binary predicates; and propositional Łukasiewicz Infinitely-valued Probabilistic Logic.

Notes

Acknowledgements

We are very thankful to Daniele Mundici for several discussions on multi-valued logics; we would also like to thank two reviewers for their very detailed comments. This work was supported by Fapesp projects 2015/21880-4 and 2014/12236-1 and CNPq grant PQ 306582/2014-7.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of São PauloSao PauloBrazil

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