Extended First-Order Logic

Authors:
Chad E. Brown;Gert Smolka
Affiliations:
Saarland University, Saarbrücken, Germany;Saarland University, Saarbrücken, Germany
Venue:
TPHOLs '09 Proceedings of the 22nd International Conference on Theorem Proving in Higher Order Logics
Year:
2009

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Abstract

We consider the EFO fragment of simple type theory, which restricts quantification and equality to base types but retains lambda abstractions and higher-order variables. We show that this fragment enjoys the characteristic properties of first-order logic: complete proof systems, compactness, and countable models. We obtain these results with an analytic tableau system and a concomitant model existence lemma. All results are with respect to standard models. The tableau system is well-suited for proof search and yields decision procedures for substantial fragments of EFO.