Deductive Bases and Interpretations

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


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.


Modal Logic Classical Logic Quantum Logic Axiom System Intuitionistic Logic 
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  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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