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It ain’t necessarily so!
Basic sequent systems for negative modalities
(João Marcos, UFRN)

We look at non-classical negations and their corresponding adjustment connectives from a modal viewpoint, over complete distributive lattices, and apply a very general mechanism in order to offer adequate analytic proof systems to logics that are based on them. Defining non-classical negations within usual modal semantics automatically allows one to treat equivalent formulas as synonymous, and to have a natural justification for a global version of the contraposition rule. From that perspective, our study offers a particularly useful environment in which negative modalities and their companions may be used for dealing with inconsistency and indeterminacy. After investigating modal logics based on arbitrary frames, we extend the results to serial frames, reflexive frames, functional frames, and symmetric frames. In each case we also investigate when and how classical negation may thereby be defined.

This is joint work with Ori Lahav and Yoni Zohar.

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  • Home
  • Videos
    • 2015 >
      • Graham Priest
      • Leon Horsten
      • Vladimir Svoboda
      • Vit Puncochar
      • David Gilbert
      • Samson Abramsky
    • NAT@Logic 2015 >
      • Valeria de Paiva
      • Dale Miller
      • Valentin Goranko
      • Ofer Arieli
      • Alessandra Palmigiano
      • Luiz Carlos Pereira
      • Guillaume Hoffmann
      • Heinrich Wansing
      • Arnon Avron
      • Joao Marcos
    • 2016 >
      • João Marcos
      • Achim Jung
      • Diana Costa
      • Samir Gorski
      • João Marcos
      • Marcos Silva
    • 2017 >
      • Catuscia Palamidessi
      • Frank Valencia
    • Filomena 2017 >
      • Tuomas Tahko
      • Jonas Becker Arenhart
      • Elaine Pimentel
    • Filomena 2019 >
      • Daniel Durante
      • Michaela McSweeney
      • Peter Verdée
  • Contact