# Note on a six-valued extension of three-valued logic

Note on a six-valued extension of three-valued logic In this paper we introduce a set of six logical values, arising in the application of three-valued logics to time intervals, find its algebraic structure, and use it to define a six-valued logic. We then prove, by using algebraic properties of the class of De Morgan algebras, that this semantically defined logic can be axiomatized as Belnap's “useful” four-valued logic. Other directions of research suggested by the construction of this set of six logical values are described. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Applied Non-Classical Logics Taylor & Francis

# Note on a six-valued extension of three-valued logic

, Volume 3 (2): 15 – Jan 1, 1993

## Note on a six-valued extension of three-valued logic

Abstract

In this paper we introduce a set of six logical values, arising in the application of three-valued logics to time intervals, find its algebraic structure, and use it to define a six-valued logic. We then prove, by using algebraic properties of the class of De Morgan algebras, that this semantically defined logic can be axiomatized as Belnap's “useful” four-valued logic. Other directions of research suggested by the construction of this set of six logical values are described.

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Publisher
Taylor & Francis
Copyright Taylor & Francis Group, LLC
ISSN
1958-5780
eISSN
1166-3081
DOI
10.1080/11663081.1993.10510806
Publisher site
See Article on Publisher Site

### Abstract

In this paper we introduce a set of six logical values, arising in the application of three-valued logics to time intervals, find its algebraic structure, and use it to define a six-valued logic. We then prove, by using algebraic properties of the class of De Morgan algebras, that this semantically defined logic can be axiomatized as Belnap's “useful” four-valued logic. Other directions of research suggested by the construction of this set of six logical values are described.

### Journal

Journal of Applied Non-Classical LogicsTaylor & Francis

Published: Jan 1, 1993

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