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- W4387618095 abstract "Residuated basic logic (RBL) is the logic of residuated basic algebras, which constitutes a conservative extension of basic propositional logic (BPL). The basic implication is a residual of a non-associative binary operator in RBL. The conservativity is shown by relational semantics. A Gentzen-style sequent calculus GRBL, which is an extension of the distributive full non-associative Lambek calculus, is established for residuated basic logic. The calculus GRBL admits the mix-elimination, subformula, and disjunction properties. Moreover, the class of all residuated basic algebras has the finite embeddability property. The consequence relation of GRBL is decidable." @default.
- W4387618095 created "2023-10-14" @default.
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- W4387618095 date "2023-10-13" @default.
- W4387618095 modified "2023-10-15" @default.
- W4387618095 title "Residuated Basic Logic" @default.
- W4387618095 doi "https://doi.org/10.3390/axioms12100966" @default.
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