Modal translations in substructural logics
Copyright policy )Modal translations in substructural logics
The Gödel-Tarski translation of the intuitionistic predicate logic into S4 by prefixing \(\square\) to all subformulas is sound and faithful. The author proves a similar result for translations of the intuitionistic versions of linear logic, relevance logic and BCK-logic into their classical S4-analogs. The proof uses analysis of cut-free Gentzen-type derivations.
Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics), linear logic, translations of intuitionistic logics into modal logics, BCK-logic, Cut-elimination and normal-form theorems, analysis of cut-free Gentzen-type derivations, Modal logic (including the logic of norms), Subsystems of classical logic (including intuitionistic logic), relevance logic
Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics), linear logic, translations of intuitionistic logics into modal logics, BCK-logic, Cut-elimination and normal-form theorems, analysis of cut-free Gentzen-type derivations, Modal logic (including the logic of norms), Subsystems of classical logic (including intuitionistic logic), relevance logic
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