Titlebook: R-Calculus, II: Many-Valued Logics; Wei Li,Yuefei Sui Book 2022 Science Press 2022 Belief revision.AGM postulates.R-calculus.Gentzen deduc

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Introduction,tent theory . where . is a minimal change of . by . i.e., a maximal set of . which is consistent with . where . is a set of atoms, and . are consistent theories of first-order logic. Here, . corresponds to iterating revision . Hence, the deduction system gives a concrete revision operator which is shown to satisfy AGM postulates.

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Co-R-Calculus for PL, in . i.e., . implies . Therefore, R-calculus consists of a nonmonotonic part and a monotonic part, where the monotonic part corresponds to monotonic tableau proof system . and the nonmonotonic part corresponds to nonmonotonic tableau proof system ..

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R-Calculus for Description Logic, and .-satisfiability, respectively. Because deductions in . and . are of finite length, whether . is provable in . or . is semi-decidable, and decidable. By combining . and . into one system . is meaningful.

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