Bulletin of the Section of Logic 8 (2):99-111 (1979)

Abstract
This paper, which in its subject matter goes back to works on strongly nite logics , is concerned with the following problems: Let Cn1; Cn2 be two strongly nite logics over the same propositional language. Is the supremum of Cn1 and Cn2 also a strongly nite operation? Is any nite matrix axiomatizable by a nite set of standard rules? The rst question can be found in [9] . The second conjec- ture was formulated by Wolfgang Rautenberg, but investigations into this problem had been carried out earlier in works of many logicians . Moreover, Stephen Bloom [1] posed a conjecture stronger than that: the consequence de- termined by a nite matrix is nitely based, i.e. it is the consequence generated by a nite set of standard rules. This hypothesis was, however, disproved by Andrzej Wronski [10] . In the present paper it is shown that neither nor holds true. The negative answer to can be viewed as a generalization of the result given by Andrzej Wronski [10]
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References found in this work BETA

On Finitely Based Consequence Operations.Andrzej Wronski - 1976 - Bulletin of the Section of Logic 5 (3):106-111.

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Citations of this work BETA

2-Element Matrices.Wolfgang Rautenberg - 1981 - Studia Logica 40 (4):315 - 353.

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