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Reports on Mathematical Logic

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No. 29 (1995)

Aldo V. FIGALLO and Paolo LANDINI

ON GENERALIZED I-ALGEBRAS AND 4-VALUED MODAL ALGEBRAS
A b s t r a c t.
In this paper we establish a new characterization of
4-valued modal algebras considered by A. Monteiro. In order
to obtain this characterization we introduce a new class of
algebras named generalized I-algebras. This class contains
strictly the class of C-algebras defined by Y. Komori as an
algebraic counterpart of the infinite-valued implicative
Lukasiewicz propositional calculus. On the other hand, the
relationship between I-algebras and commutative
BACK-algebras, defined by S. Tanaka in 1975, allows us to say
that in a certain sense G-algebras are also a generalization of
these latter algebras.

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