The completeness of S

Studia Logica 38 (2):137 - 147 (1979)
The subsystem S of Parry's AI [10] (obtained by omitting modus ponens for the material conditional) is axiomatized and shown to be strongly complete for a class of three valued Kripke style models. It is proved that S is weakly complete for the class of consistent models, and therefore that Ackermann's rule is admissible in S. It also happens that S is decidable and contains the Lewis system S4 on translation — though these results are not presented here. S is arguably the most relevant relevant logic known at this time to be decidable.
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DOI 10.1007/BF00370438
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References found in this work BETA
J. Michael Dunn (1972). A Modification of Parry's Analytic Implication. Notre Dame Journal of Formal Logic 13 (2):195-205.

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Thomas Macaulay Ferguson (2014). A Computational Interpretation of Conceptivism. Journal of Applied Non-Classical Logics 24 (4):333-367.
Harry Deutsch (1984). Paraconsistent Analytic Implication. Journal of Philosophical Logic 13 (1):1 - 11.

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