On the degree of complexity of sentential logics. A couple of examples

Studia Logica 40 (2):141 - 153 (1981)
The first part of the paper is a reminder of fundamental results connected with the adequacy problem for sentential logics with respect to matrix semantics. One of the main notions associated with the problem, namely that of the degree of complexity of a sentential logic, is elucidated by a couple of examples in the second part of the paper. E.g., it is shown that the minimal logic of Johansson and some of its extensions have degree of complexity 2. This is the first example of an exact estimation of the degree of natural complex logics, i.e. logics whose deducibility relation cannot be represented by a single matrix. The remaining examples of complex logics are more artificial, having been constructed for the purpose of checking some theoretical possibilities.
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DOI 10.1007/BF01874705
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Decidability of S4.Krister Segerberg - 1968 - Theoria 34 (1):7-20.
A Matrix Adequate for S5 with Mp and Rn.Jacek Hawranek - 1980 - Bulletin of the Section of Logic 9 (3):122-123.

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A Gentzen System for Conditional Logic.Fernando Guzmán - 1994 - Studia Logica 53 (2):243 - 257.

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