Term-Generic Logic

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5486)


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.


Free Variable Proof System Atomic Formula Relation Symbol Deduction Rule 
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© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of Illinois at Urbana-ChampaignUSA

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