Opis

• Tytuł:
  Super-Strict Implications
• Twórca:
  Gherardi, Guido;
  Orlandelli, Eugenio
• Współtwórca:
  Gherardi, Guido - University of Bologna, Department of Philosophy and Communication Studies I-40126, Via Zamboni 38, Bologna, Italy;
  Orlandelli, Eugenio - University of Bologna, Department of Philosophy and Communication Studies I-40126, Via Zamboni 38, Bologna, Italy;
  Gherardi, Guido - guido.gherardi@unibo.it;
  Orlandelli, Eugenio - eugenio.orlandelli@unibo.it
• Opis:
  This paper introduces the logics of super-strict implications, where a super-strict implication is a strengthening of C.I. Lewis' strict implication that avoids not only the paradoxes of material implication but also those of strict implication. The semantics of super-strict implications is obtained by strengthening the (normal) relational semantics for strict implication. We consider all logics of super-strict implications that are based on relational frames for modal logics in the modal cube. it is shown that all logics of super-strict implications are connexive logics in that they validate Aristotle's Theses and (weak) Boethius's Theses. A proof-theoretic characterisation of logics of super-strict implications is given by means of G3-style labelled calculi, and it is proved that the structural rules of inference are admissible in these calculi. It is also shown that validity in the S5-based logic of super-strict implications is equivalent to validity in G. Priest's negation-as-cancellation-based logic. Hence, we also give a cut-free calculus for Priest's logic.
• Dostępność obiektu:
  Dostęp otwarty
• Prawa: https://creativecommons.org/licenses/by-nc-nd/4.0
• Data:
  2021.05.05;
  2021.01.20
• Typ:
  Other
• Język:
  angielski
• Format:
  application/pdf
• Wydawca:
  Wydawnictwo Uniwersytetu Łódzkiego
• Relacja:
  Bulletin of the Section of Logic;1;
  50
• Temat i słowa kluczowe:
  Strict implication;
  paradoxes of implication;
  connexive implication;
  sequent calculi;
  structural rules
• Identyfikator:
  0138-0680;
  http://hdl.handle.net/11089/35350 ;
  2449-836X;
  10.18778/0138-0680.2021.02
• Dostawca danych:
  Repozytorium Uniwersytetu Łódzkiego
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