Abstract

Since the seminal paper by J. McCarthy [2], three-valued logic is the standard tool to study the behaviour of the sequential boolean operators: a special value ? denotes the result of undefined computations. In this paper we propose an more precise approach based on a multi-valued logic, in order to distinguish between several types of discernible errors. We present two results about the equational axiomatizability of boolean op'erators in multivalued logics: one is about the signature if \Gamma then \Gamma else; true; false (the three-valued case was presented by J. McCarthy in 1963), and the other one about the classical signature and; or; not; true; false (similar to the result obtained by Guzm`an and Squier in 1990). R'esum'e Depuis l'article fondateur de J. McCarthy [2] l"etude des comportement des op'erateurs bool'eens s'equentiels a 'et'e men'ee grace `a la logique trivalu'ee, dans laquelle une valeur sp'eciale ? repr'esente le r'esultat d'une 'evaluation ind'etermin'ee. Nous...

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