|Title:||On evaluations of propositional formulas in countable structures||Journal:||Filomat||Volume:||30||Issue:||1||First page:||1||Last page:||13||Issue Date:||1-Jan-2016||Rank:||M22||ISSN:||0354-5180||DOI:||10.2298/FIL1601001P||Abstract:||
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 purpose of such a formalism is to provide a general propositional framework for reasoning about F-valued evaluations of propositional formulas, where F is a C-valued L-structure. The prime examples of F are the field of rational numbers Q, its countable elementary extensions, its real and algebraic closures, the field of fractions Q(Ɛ), where " is a positive infinitesimal and so on.
|Keywords:||Axiomatization | Strong completeness | Weighted formulas||Publisher:||Faculty of Sciences and Mathematics, University of Niš, Serbia|
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