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The expressive unary truth functions of \(n\)-valued logic. (English) Zbl 1098.03032
To every (normal) consequence relation there corresponds a notion of closure such that the set of closed sets forms a complete lattice. If the consequence relation is finitary, this lattice has a minimal closed basis consisting of the irreducibles [see R. Wójcicki, Theory of logical caculi. Basic theory of consequence operations. Dordrecht: Kluwer Academic Publishers (1988; Zbl 0682.03001)]. If all these irreducibles are maximally consistent, the lattice is said to be expressive. Some truth functions force irreducibles to be maximally consistent and hence are called expressive. In “The expressive truth conditions of two-valued logic” [Notre Dame J. Formal Logic 43, 221–230 (2002; Zbl 1050.03008)] the author has identified all expressive truth functions of two-valued logic. This paper identifies the expressive truth functions of \(n\)-valued logic, by characterizing the unary ones.
MSC:
03B50 Many-valued logic
03B22 Abstract deductive systems
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