Computations in Boolean algebra extended by adding an undefined element are investigated in the present paper. These computations (also known as approximative computations) are based on Lukasiewicz three-valued logic and are widely used in those applications where it is necessary to perform logical operations under uncertainty. The approximative computations are carried out as follows: if all instantiations of undefined operands produce the same result then this ascertained result is taken as final; otherwise, the final result is defined to be unknown. The key question in theory of approximative computations is whether a given Boolean formula is closed in the sense that the stepwise approximative computations in compliance with a given formula produce a result as accurate as possible. This question is investigated for the classes of disjunctive and algebraic normal forms.
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