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Classical C-systems: Logical achievements and logical problems (2015)
(Arnon Avron, Tel Aviv University, IL)

What is a classical LFI, and when are two such logics identical?

We discuss two fundamental questions concerning classical LFIs (i.e., LFIs which are based on positive classical logic). We start with the observation that according to the official definition, an axiomatic extension of classical logic is an LFI w.r.t some unary connective *iff it has a bottom element, and * satisfies three simple minimal conditions (that, for atomic P, neither of P and *P implies the other, and their conjunction does not implies the bottom element). This means that the class of classical LFIs is rather broad in comparison to the family of logics on which most of the investigations on LFIs have concentrated on. Accordingly, we provide a characterization of this family.

Another question that we address is when should we see two LFIs as identical. For example: is da Costa $C_1$ identical with the  system $Cila$x, or $Cla$? Our reply is that with neither. 

To provide adequate answers to both questions we describe and use appropriate semantic and proof-theoretical tools.

Click for slides.
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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