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p-Adic Multiple-Validity and p-Adic Valued Logical Calculi
Andrew Schumann

In this paper, I introduce a new idea of p-adic many-validity to construct p-adic valued matrix logic M Zp and p-adic valued propositional logical calculi: p-adic valued logic of Hilbert’s type, p-adic valued sequent logic, and p-adic valued hypersequent logic. These logical systems are considered for the first time. Notice that as a result p-adic valued probability theory and p-adic valued fuzzy logic can be constructed on the base of p-adic valued matrix logic. The complexity of the problem of setting p-adic valued probability and p-adic valued fuzziness consists in that a Boolean algebra is a logical lattice for real-valued probability and fuzziness. This algebra cannot be a logical lattice for p-adic valued fuzzy and probabilistic reasoning.

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