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Kikuchi, Kentaro; Sasaki, Katsumi

doi:10.1023/a:1022363219134

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2007

2023

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Cited by 6 publications

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“…Visser's propositional logics have been studied in, e.g., [6,[9][10][11][12][13]. In the proof-theoretic respect, Gentzen-style sequent calculi for basic propositional logics are given in [14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Residuated Basic Logic

Lin,

2023

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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.

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