Abstract
In the classical context, the notion of consequence can be equivalently presented by consequence operator approach and consequence relation approach. Similar approaches are observed in fuzzy context too. Different proposals came up in order to bridge the gap between Pavelka’s notion of fuzzy consequence operator and Chakraborty’s notion of graded consequence relation in fuzzy context. In this regard, we shall discuss the notion of fuzzy consequence relation by Castro et al., and implicative consequence operator and implicative consequence relation by Rodríguez et al. We shall discuss some of the limitations of these approaches, and propose extensions of fuzzy consequence relation of Castro et al., and the notion of implicative consequence relation of Rodríguez et al, in a graded meta-language. In both the cases, the notion of graded consequence with fuzzy set of premises is considered.
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Chakraborty, M.K., Dutta, S. (2019). Meta-logical Notions Generalized: Graded Consequence with Fuzzy Set of Premises. In: Theory of Graded Consequence. Logic in Asia: Studia Logica Library. Springer, Singapore. https://doi.org/10.1007/978-981-13-8896-5_5
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