Studia Logica 38 (2):137 - 147 (1979)
The subsystem S of Parry's AI  (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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References found in this work BETA
A Modification of Parry's Analytic Implication.J. Michael Dunn - 1972 - Notre Dame Journal of Formal Logic 13 (2):195-205.
Citations of this work BETA
Logics of Nonsense and Parry Systems.Thomas Macaulay Ferguson - 2015 - Journal of Philosophical Logic 44 (1):65-80.
A Computational Interpretation of Conceptivism.Thomas Macaulay Ferguson - 2014 - Journal of Applied Non-Classical Logics 24 (4):333-367.
Paraconsistent Analytic Implication.Harry Deutsch - 1984 - Journal of Philosophical Logic 13 (1):1 - 11.
A Note on the Decidability of a Strong Relevant Logic.Harry Deutsch - 1985 - Studia Logica 44 (2):159 - 164.
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