The logic of Chang’s algebra

Author: Revaz Grigolia
Co-authors: A. Di Nola
Keywords: Lukasievicz logic, Chang's algebra, MV-algebra
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It is introduced the new logic QC - the logic of Chang’s algebra, which is an extension of the infinitely valued Lukasiewicz logic L, the language of which enriched by 0-ary connective c that is interpreted as "qvasi-false", the algebraic counterpart of which are algebras from a qvasi-variety of the variety generated by the perfect MV -algebras. For this aim we introduce a new class QC of QC-algebras which is a quasi-variety. Adding a new inference rule to the logic QC, thereby increased a deducibility power, we introduce the logic QC+ and defining the notion of quasi-true (q-true) formulas it is proved the completeness theorem for this logic.