Notre Dame Journal of Formal Logic

Finite Tree Property for First-Order Logic with Identity and Functions

Merrie Bergmann

Abstract

The typical rules for truth-trees for first-order logic without functions can fail to generate finite branches for formulas that have finite models–the rule set fails to have the finite tree property. In 1984 Boolos showed that a new rule set proposed by Burgess does have this property. In this paper we address a similar problem with the typical rule set for first-order logic with identity and functions, proposing a new rule set that does have the finite tree property.

Article information

Source
Notre Dame J. Formal Logic Volume 46, Number 2 (2005), 173-180.

Dates
First available in Project Euclid: 2 June 2005

Permanent link to this document
http://projecteuclid.org/euclid.ndjfl/1117755148

Digital Object Identifier
doi:10.1305/ndjfl/1117755148

Mathematical Reviews number (MathSciNet)
MR2150950

Zentralblatt MATH identifier
1078.03044

Subjects
Primary: 03B10: Classical first-order logic 03F03: Proof theory, general

Keywords
finite tree property truth-trees

Citation

Bergmann, Merrie. Finite Tree Property for First-Order Logic with Identity and Functions. Notre Dame Journal of Formal Logic 46 (2005), no. 2, 173--180. doi:10.1305/ndjfl/1117755148. http://projecteuclid.org/euclid.ndjfl/1117755148.


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References

  • [1] Bergmann, M., J. Moor, and J. Nelson, The Logic Book, McGraw-Hill, New York, 1998.
  • [2] Boolos, G., "Trees and finite satisfiability: Proof of a conjecture of Burgess", Notre Dame Journal of Formal Logic, vol. 25 (1984), pp. 193--97.
  • [3] Hintikka, J., "Form and content in quantification theory", Acta Philosophica Fennica, vol. 8 (1955), pp. 7--55.
  • [4] Hintikka, J., "Notes on the quantification theory", Societas Scientiarum Fennica. Commentationes Physico-Mathematicae, vol. 17 (1955), no. 12, 13 pp.
  • [5] Smullyan, R. M., First-Order Logic, Dover Publications, Inc., New York, 1995. Corrected reprint of the 1968 original.