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Journal of Logic and Computation 1991 1(6):797-810; doi:10.1093/logcom/1.6.797
© 1991 by Oxford University Press
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Original Articles

Kleene's Logic, Generalized

MELVIN FITTING

Dept. Mathematics and Computer Science Lehman College (CUNY) Bronx, NY 10468; Depts. Computer Science, Philosophy, Mathematics Graduate Center (CUNY) 33 West 42nd Street, NYC, NY 10036

Kleene's well-known strong three-valued logic is shown to be one of a family of logics with similar mathematical properties. These logics are produced by an intuitively natural construction. The resulting logics have direct relationships with bilattices. In addition they prossess mathematical features that lend themselves well to semantical constructions based on fixpoint procedures, as in logic programming.


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