Notre Dame Journal of Formal Logic

Semantics-based Nonmonotonic Inference

Heinrich Wansing

Abstract

In this paper we discuss Gabbay's idea of basing nonmonotonic deduction on semantic consequence in intuitionistic logic extended by a consistency operator and Turner's suggestion of replacing the intuitionistic base system by Kleene's three-valued logic. It is shown that a certain counterintuitive feature of these approaches can be avoided by using Nelson's constructive logic N instead of intuitionistic logic or Kleene's system. Moreover, in N a more general notion of consistency can be defined and nonmonotonic deduction can thus be based on a logical system satisfying the Deduction Theorem.

Article information

Source
Notre Dame J. Formal Logic, Volume 36, Number 1 (1995), 44-54.

Dates
First available in Project Euclid: 19 December 2002

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1040308828

Digital Object Identifier
doi:10.1305/ndjfl/1040308828

Mathematical Reviews number (MathSciNet)
MR1359107

Zentralblatt MATH identifier
0839.03012

Subjects
Primary: 03B20: Subsystems of classical logic (including intuitionistic logic)
Secondary: 03B50: Many-valued logic 03B60: Other nonclassical logic 68T27: Logic in artificial intelligence

Citation

Wansing, Heinrich. Semantics-based Nonmonotonic Inference. Notre Dame J. Formal Logic 36 (1995), no. 1, 44--54. doi:10.1305/ndjfl/1040308828. https://projecteuclid.org/euclid.ndjfl/1040308828


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References

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