Graded Consequence and Some Metalogical Notions Generalized

Article type: Research Article

Authors: Chakraborty, Mihir K. | Basu, Sanjukta

Affiliations: Department of Pure Mathematics, University of Calcutta, 35, Ballygunge Circular Road, Calcutta 700 019, India. itbpc@gems.vsnl.net.in

Abstract: The notion of graded consequence and some other metalogical notions like consistency, inconsistency, tautologihood and theoremhood to which grades have been introduced earlier by us are reviewed in the context of generalized operators. Some preliminary results regarding the relation between the notion of graded consequence and the notion of graded inconsistency are proved. The method of axiomatization is reconsidered in this general situation.

Keywords: Fuzzy set, fuzzy logic, graded consequence, residuated lattice

DOI: 10.3233/FI-1997-323405

Journal: Fundamenta Informaticae, vol. 32, no. 3-4, pp. 299-311, 1997