Notre Dame Journal of Formal Logic

Biconsequence Relations: A Four-Valued Formalism of Reasoning with Inconsistency and Incompleteness

Alexander Bochman

Abstract

We suggest a general formalism of four-valued reasoning, called biconsequence relations, intended to serve as a logical framework for reasoning with incomplete and inconsistent data. The formalism is based on a four-valued semantics suggested by Belnap. As for the classical sequent calculus, any four-valued connective can be defined in biconsequence relations using suitable introduction and elimination rules. In addition, various three-valued and partial logics are shown to be special cases of this formalism obtained by imposing appropriate additional logical rules. We show also that such rules are instances of a single logical principle called coherence. The latter can be considered a general requirement securing that the information we can infer in this framework will be classically coherent.

Article information

Source
Notre Dame J. Formal Logic Volume 39, Number 1 (1998), 47-73.

Dates
First available in Project Euclid: 7 December 2002

Permanent link to this document
http://projecteuclid.org/euclid.ndjfl/1039293020

Mathematical Reviews number (MathSciNet)
MR1671730

Digital Object Identifier
doi:10.1305/ndjfl/1039293020

Zentralblatt MATH identifier
0967.03019

Subjects
Primary: 03B50: Many-valued logic
Secondary: 68T27: Logic in artificial intelligence

Citation

Bochman, Alexander. Biconsequence Relations: A Four-Valued Formalism of Reasoning with Inconsistency and Incompleteness. Notre Dame Journal of Formal Logic 39 (1998), no. 1, 47--73. doi:10.1305/ndjfl/1039293020. http://projecteuclid.org/euclid.ndjfl/1039293020.


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