Abstract
The paper introduces a notion of an algebra corresponding to the three-valued logical calculus designed by McCarthy for computation purposes and used in several existing software system. The algebra, called McCarthy algebra, is a generalization of a Boolean algebra. It is defined extensionally, but a set of sound equality axioms is also given. From these axioms, various non-classical properties of the elements of such algebras are deduced. A representation theorem for two classes of McCarthy algebras is presented.
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