Term-Generic Logic

  • Andrei Popescu
  • Grigore Roşu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5486)

Abstract

Term-generic logic (TGL) is a first-order logic parameterized with terms defined axiomatically (rather than constructively), by requiring them to only provide generic notions of free variable and substitution satisfying reasonable properties. TGL has a complete Gentzen system generalizing that of first-order logic. A certain fragment of TGL, called Horn 2, possesses a much simpler Gentzen system, similar to traditional typing derivation systems of λ-calculi. Horn 2 appears to be sufficient for defining a whole plethora of λ-calculi as theories inside the logic. Within intuitionistic TGL, a Horn 2 specification of a calculus is likely to be adequate by default. A bit of extra effort shows adequacy w.r.t. classic TGL as well, endowing the calculus with a complete loose semantics.

Keywords

Free Variable Proof System Atomic Formula Relation Symbol Deduction Rule 
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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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Andrei Popescu
    • 1
  • Grigore Roşu
    • 1
  1. 1.Department of Computer ScienceUniversity of Illinois at Urbana-ChampaignUSA

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