|Affiliations:||Mathematical Institute of the Serbian Academy of Sciences and Arts||Title:||On evaluations of propositional formulas whose range is a subset of some fixed countable ordered field||Journal:||World Scientific Proc. Series on Computer Engineering and Information Science 7; Uncertainty Modeling in Knowledge Engineering and Decision Making - Proceedings of the 10th International FLINS Conf.||Volume:||7||First page:||567||Last page:||572||Conference:||10th International Fuzzy Logic and Intelligent Technologies inNuclear Science Conference, FLINS 2012; Istanbul; Turkey; 26 August 2012 through 29 August 2012||Editors:||Kahraman, Cengiz
Tunc Bozbura, Faik
Kerre, Etienne E.
Let L be a countable first-order language such that its set of constant symbols Const(L) is countable. We provide a complete infinitary propositional logic (formulas remain finite sequences of symbols, but we use inference rules with countably many premises) for description of C-valued L-structures, where C is an infinite subset of Const(L). The main goal is to provide a formal framework for reasoning about F-valued evaluations of propositional formulas, where F is some countable ordered field. The prime examples of F are the field of rational numbers ℚ, its real closure ℚ and the field of fractions ℚ(ε), where ε is a positive infinitesimal.
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