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Deductive Bases and Interpretations

  • Ryszard Wójcicki
Part of the Synthese Library book series (SYLI, volume 199)

Abstract

Rules of inference are divided into H-rules (Hilbert style) and G-rules (Gentzen style). Modus Ponens (MP: α, αββ) is an example of an H-rule, the Deduction Rule (DT: X, αβ/Xαβ; read: from X infer αβ, provided that β has been inferred from X ∪ {α}) is a G-ruule. An H-rule R is a rule of C (sound for C) if all theories of C are preserved under R. A G-rule is a rule of C if it preserves ⊢ c.

Keywords

Modal Logic Classical Logic Quantum Logic Axiom System Intuitionistic Logic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 8.
    For rigorous definitions of introduction and elimination rules see e.g. Prawitz [1965].Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1988

Authors and Affiliations

  • Ryszard Wójcicki
    • 1
  1. 1.Section of Logic, Institute of Philosophy and SociologyPolish Academy of SciencesPoland

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