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  1.  31
    Characterizing Equivalential and Algebraizable Logics by the Leibniz Operator.Burghard Herrmann - 1997 - Studia Logica 58 (2):305-323.
    In [14] we used the term finitely algebraizable for algebraizable logics in the sense of Blok and Pigozzi [2] and we introduced possibly infinitely algebraizable, for short, p.i.-algebraizable logics. In the present paper, we characterize the hierarchy of protoalgebraic, equivalential, finitely equivalential, p.i.-algebraizable, and finitely algebraizable logics by properties of the Leibniz operator. A Beth-style definability result yields that finitely equivalential and finitely algebraizable as well as equivalential and p.i.-algebraizable logics can be distinguished by injectivity of the Leibniz operator. Thus, (...)
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  2.  22
    Equivalential and Algebraizable Logics.Burghard Herrmann - 1996 - Studia Logica 57 (2-3):419 - 436.
    The notion of an algebraizable logic in the sense of Blok and Pigozzi [3] is generalized to that of a possibly infinitely algebraizable, for short, p.i.-algebraizable logic by admitting infinite sets of equivalence formulas and defining equations. An example of the new class is given. Many ideas of this paper have been present in [3] and [4]. By a consequent matrix semantics approach the theory of algebraizable and p.i.-algebraizable logics is developed in a different way. It is related to the (...)
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  3.  24
    Algebraizability and Beth's Theorem for Equivalential Logics.Burghard Herrmann - 1993 - Bulletin of the Section of Logic 22:85-88.