Abstract
In this chapter, a logical connective negation (\(\lnot \)) is introduced in the object language, and the set of axioms for characterizing a graded consequence relation is extended in the presence of \(\lnot \). An axiomatic approach to the notion of graded inconsistency is also introduced, and an equivalence between the notions of graded consequence and graded inconsistency is established. In continuation to the study of level cuts of a graded consequence relation, presented in Chap. 2, a few results considering \(\lnot \) in the language are also presented. Reflection of the newly added axioms in the meta-level algebraic structure is explored in an extended algebraic structure of a complete residuated lattice. The properties of this structure, called GC(\(\lnot \))-algebra, are studied as well.
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Chakraborty, M.K., Dutta, S. (2019). Introducing Negation (\(\lnot \)) in the Object Language of the Theory of Graded Consequence. In: Theory of Graded Consequence. Logic in Asia: Studia Logica Library. Springer, Singapore. https://doi.org/10.1007/978-981-13-8896-5_3
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DOI: https://doi.org/10.1007/978-981-13-8896-5_3
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