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Analytic Calculi for Non-Classical Logics: Theory and Applications (Invited Talk)

Author Agata Ciabattoni

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  • Proof theory
  • Fuzzy logic

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Abstract

The possession of a suitable proof-calculus is the starting point for many investigations into a logic, including decidability and complexity, computational interpretations and automated theorem proving. By suitable proof-calculus we mean a calculus whose proofs exhibit some notion of subformula property ("analyticity"). In this talk we describe a method for the algorithmic introduction of analytic sequent-style calculi for a wide range of non-classical logics starting from Hilbert systems. To demonstrate the widespread applicability of this method, we discuss how to use the introduced calculi for proving various results ranging from Curry-Howard isomorphism to new interpretative tools for Indology.

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Agata Ciabattoni. Analytic Calculi for Non-Classical Logics: Theory and Applications (Invited Talk). In 25th EACSL Annual Conference on Computer Science Logic (CSL 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 62, p. 4:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016) https://doi.org/10.4230/LIPIcs.CSL.2016.4

Author Details

Agata Ciabattoni

References

  1. Federico Aschieri, Agata Ciabattoni, and Francesco A. Genco. Curry-Howard Correspondance for Goedel Logic: from Natural Deduction to Parallel Computation. Submitted. Google Scholar
  2. Agata Ciabattoni, Elisa Freschi, Francesco A. Genco, and Björn Lellmann. Mīmāmsā deontic logic: Proof theory and applications. In Automated Reasoning with Analytic Tableaux and Related Methods - 24th International Conference, TABLEAUX 2015, Wrocław, Poland, September 21-24, 2015. Proceedings, pages 323-338, 2015. Google Scholar
  3. Agata Ciabattoni, Nikolaos Galatos, and Kazushige Terui. From axioms to analytic rules in nonclassical logics. In Proceedings of the Twenty-Third Annual IEEE Symposium on Logic in Computer Science, LICS 2008, 24-27 June 2008, Pittsburgh, PA, USA, pages 229-240, 2008. Google Scholar
  4. Agata Ciabattoni and Revantha Ramanayake. Power and limits of structural display rules. ACM TOCL, 17(3), 2016. Google Scholar
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