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

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.