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Plug and Play Negations

  • Sérgio Marcelino
  • Carlos Caleiro
  • Umberto Rivieccio
Chapter
Part of the Trends in Logic book series (TREN, volume 47)

Abstract

We study an array of logics defined on a small set of connectives (including an implication \(\rightarrow \) and a bottom particle \(\bot \)) by modularly considering subsets of a set of inference rules that we fix at the start of the game. We provide complete semantics based on possibly non-deterministic logical matrices and complexity upper bounds for the considered logics. As a consequence of the techniques applied, we also obtain completeness results for the negation-only fragments (obtained by defining the negation connective as \(\lnot p:=p\rightarrow \bot \), as usual) of all the above-mentioned logics, and analyze their possible paraconsistent character.

Notes

Acknowledgements

The first two authors thank the support of the FEDER/FCT project PEst-OE/EEI/LA0008/2013 of Instituto de Telecomunicações. The first author also acknowledges the FCT postdoctoral grant SFRH/BPD/76513/2011. Finally, we would like to thank Fey Liang for pointing out a deadly mistake in an earlier version of the paper.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Sérgio Marcelino
    • 1
  • Carlos Caleiro
    • 1
  • Umberto Rivieccio
    • 2
  1. 1.SQIG - Instituto de Telecomunicações, Dep. Matemática – Instituto Superior TécnicoUniv. LisboaLisboaPortugal
  2. 2.Dep. Informática e Matemática AplicadaUniv. Federal do Rio Grande do NorteNatalBrazil

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