Notre Dame Journal of Formal Logic

Ontologically Minimal Logical Semantics

Uwe Meixner

Abstract

Ontologically minimal truth law semantics are provided for various branches of formal logic (classical propositional logic, S5 modal propositional logic, intuitionistic propositional logic, classical elementary predicate logic, free logic, and elementary arithmetic). For all of them logical validity/truth is defined in an ontologically minimal way, that is, not via truth value assignments or interpretations. Semantical soundness and completeness are proved (in an ontologically minimal way) for a calculus of classical elementary predicate logic.

Article information

Source
Notre Dame J. Formal Logic, Volume 36, Number 2 (1995), 279-298.

Dates
First available in Project Euclid: 18 December 2002

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1040248459

Digital Object Identifier
doi:10.1305/ndjfl/1040248459

Mathematical Reviews number (MathSciNet)
MR1345749

Zentralblatt MATH identifier
0835.03003

Subjects
Primary: 03Bxx: General logic

Citation

Meixner, Uwe. Ontologically Minimal Logical Semantics. Notre Dame J. Formal Logic 36 (1995), no. 2, 279--298. doi:10.1305/ndjfl/1040248459. https://projecteuclid.org/euclid.ndjfl/1040248459


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References

  • Field, H., “Realism, mathematics and modality,” pp. 227–281 in H. Field, Realism, Mathematics and Modality, Blackwell, Oxford, 1989.
  • Field, H., “Metalogic and modality,” Philosophical Studies, vol. 62 (1991), pp. 1–22. MR 92j:03002
  • Hughes, G. E., and M. J. Cresswell, An Introduction to Modal Logic, Methuen, London, 1974. Zbl 0205.00503 MR 55:12472
  • Leblanc, H., “On dispensing with things and worlds,” pp. 241–259 in Logic and Ontology, edited by M. K. Munitz, New York University Press, New York, 1973.
  • Meixner, U., “An alternative semantics for modal predicate- logic,” Erkenntnis, vol. 37 (1992), pp. 377–400. MR 93m:03030
  • Smullyan, R., First-order Logic, Springer-Verlag, Berlin, 1968. Zbl 0172.28901 MR 39:5311