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A Focused Sequent Calculus for Higher-Order Logic

  • Fredrik Lindblad
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8562)

Abstract

We present a focused intuitionistic sequent calculus for higher-order logic. It has primitive support for equality and mixes λ-term conversion with equality reasoning. Classical reasoning is enabled by extending the system with rules for reductio ad absurdum and the axiom of choice. The resulting system is proved sound with respect to Church’s simple type theory. The soundness proof has been formalized in Agda. A theorem prover based on bottom-up search in the calculus has been implemented. It has been tested on the TPTP higher-order problem set with good results. The problems for which the theorem prover performs best require higher-order unification more frequently than the average higher-order TPTP problem. Being strong at higher-order unification, the system may serve as a complement to other theorem provers in the field.

Keywords

Inference Rule Theorem Prover Natural Deduction Sequent Calculus Derivation Tree 
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 International Publishing Switzerland 2014

Authors and Affiliations

  • Fredrik Lindblad
    • 1
  1. 1.Chalmers University of TechnologyUniversity of GothenburgGothenburgSweden

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