Bounded Lukasiewicz Logics
نویسندگان
چکیده
In this work we investigate bounded Lukasiewicz logics, characterised as the intersection of the k-valued Lukasiewicz logics for k = 2, . . . , n (n ≥ 2). These logics formalise a generalisation of Ulam’s game with applications in Information Theory. Here we provide an analytic proof calculus G LBn for each bounded Lukasiewicz logic, obtained by adding a single rule to G L, a hypersequent calculus for Lukasiewicz infinite-valued logic. We give a first cut-elimination proof for G L with (suitable forms of) cut rules. We then prove completeness for G LBn with cut and show that cut can also be eliminated in this case.
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We consider propositional logic. Three-valued logics are old: the first one is Lukasiewicz three valued logic from 1920 [8]. Gödel in [5] from 1932 studied a hierarchy of finite-valued logics, containing Gödel three-valued logic. Our main interest pays to Kleene three-valued logic [6]. Other threevalued logics will not be considered here. Let us agree that the three truth values are 0, 1 2 , 1 ...
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