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Usually the number of truth-values and the meanings of operators in a given axiom set for many-valued logic are not defined explicitly but done implicitly by many formulas derived from the set. However, it is very laborious to determine them. In this paper, axioms and undefined operators are treated as logical equations and unknown logical functions… (More)
By using the method of indeterminate coefficients, we can examine the independence of each axiom of a system of axioms. In this paper, we treat the Russell's classical logical system of axioms. We examine whether each axiom is independent or not from the other axioms and show the results.
By using the Method of lndeterminate Coefficients, we can clarify the fundamental properties of axioms of Kleene algebra, especially derive finite models of the algebra. In this paper, we transform the logical equations to those including one kind of unknown logical function. Finally, all models of kleene algebra of 9 elements are derived