Completeness and Decidability of General First-Order Logic

Journal of Philosophical Logic 46 (3):233-257 (2017)
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Abstract

This paper investigates the “general” semantics for first-order logic introduced to Antonelli, 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. :217–274, 1998), thereby showing the former decidable. A truth-tree method is presented in the Appendix.

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10.1007/s10992-016-9421-y

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G. Aldo Antonelli
University of California, Davis

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References found in this work

First-order logic.Raymond Merrill Smullyan - 1968 - New York [etc.]: Springer Verlag.
English as a Formal Language.Richard Montague - 1970 - In Bruno Visentini (ed.), Linguaggi nella societa e nella tecnica. Edizioni di Communita. pp. 188-221.
Completeness in the theory of types.Leon Henkin - 1950 - Journal of Symbolic Logic 15 (2):81-91.
On a generalization of quantifiers.Andrzej Mostowski - 1957 - Fundamenta Mathematicae 44 (2):12--36.
First-order Logic.William Craig - 1975 - Journal of Symbolic Logic 40 (2):237-238.

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