Journal of Philosophical Logic

, Volume 46, Issue 3, pp 233–257

Completeness and Decidability of General First-Order Logic (with a Detour Through the Guarded Fragment)

  • Aldo Antonelli
Article

DOI: 10.1007/s10992-016-9421-y

Cite this article as:
Antonelli, A. J Philos Logic (2017) 46: 233. doi:10.1007/s10992-016-9421-y

Abstract

This paper investigates the “general” semantics for first-order logic introduced to Antonelli (Review of Symbolic Logic 6(4), 637–58, 2013): a sound and complete axiom system is given, and the satisfiability problem for the general semantics is reduced to the satisfiability of formulas in the Guarded Fragment of Andréka et al. (Journal of Philosophical Logic 27(3):217–274, 1998), thereby showing the former decidable. A truth-tree method is presented in the Appendix.

Keywords

First-order quantifiers Decidability General semantics 

Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  • Aldo Antonelli
    • 1
  1. 1.Department of PhilosophyUniversity of California, DavisDavisUSA

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