UNIQUENESS OF THE FIXED POINTS OF SINGLE–STEP OPERATORS DETERMINED BY BELNAP’S¹ FOUR–VALUED LOGICS

Eleanor Clifford – Anthony Karel Seda

   Recently, Hitzler and Seda showed how a domain-theoretic proof can be given of the fact that, for a locally hierarchical program, the single-step operator T_P, defined in two-valued logic, has a unique fixed point. Their approach employed a construction which turned a Scott-Ershov domain into a generalized ultrametric space. Finally, a fixed-point theorem of Priess-Crampe and Ribenboim was applied to T_P to establish the result. In this paper, we extend these methods and results to the corresponding well-known single-step operators Φ_P and Ψ_P determined by P and defined, respectively, in three-valued and four-valued logics.

Keywords: fixed point, operator, many-valued logic, Scott-Ershov domain, locally hierarchical program

[full-paper]