Abstract
It is shown that there exists no grammatical translation into classical (propositional) logic of the modal logics, nor of intuitionistic logic and of the relatedness and dependence logics, as defined in Richard L. Epstein's bookThe Semantic foundations of logic. In the book the result is proved for translations without parameters.
Classical propositional logicPC can be translated into other logics. Usually the grammatical structure of propositions is preserved, in the sense of the following definition.
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References
[E] Epstein, R.L. (with the assistance and collaboration of Carnielli, W., Ottaviano, M.L.D., Krajewski, S., Muddox, R.D.). The Semantic Foundations of Logic. Volume I: Propositional Logics, Amsterdam: Nijhof 1990
[K] Krajewski, S.: One logic or many logics? Epstein's set-assignment semantics for logical calculi. J. Non-Classical Logic (to appear)
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Krajewski, S. Note on grammatical translations of logical calculi. Arch Math Logic 31, 259–262 (1992). https://doi.org/10.1007/BF01794982
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DOI: https://doi.org/10.1007/BF01794982