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

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

#### 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.

First Page:
Primary Subjects: 03B50
Secondary Subjects: 68T27
Full-text: Open access

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

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