First-Order Logic with Dependent Types

  • Florian Rabe
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4130)


We present DFOL, an extension of classical first-order logic with dependent types, i.e., as in Martin-Löf type theory, signatures may contain type-valued function symbols. A model theory for the logic is given that stays close to the established first-order model theory. The logic is presented as an institution, and the logical framework LF is used to define signatures, terms and formulas. We show that free models over Horn theories exist, which facilitates its use as an algebraic specification language, and show that the classical first-order axiomatization is complete for DFOL, too, which implies that existing first-order theorem provers can be extended. In particular, the axiomatization can be encoded in LF.


Free Variable Theorem Prove Type Theory Function Symbol Atomic Formula 


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© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Florian Rabe
    • 1
  1. 1.Carnegie Mellon University and International University Bremen 

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