A triangular-norm-based propositional fuzzy logic
The paper presents a formal system of fuzzy logic which based on the nilpotent minimum t-norm \(R_0\) (left-continuous non-continuous t-norm). This logic is a special case of the MTL-fuzzy logic (monoidal t-norm-based). The underlying algebra of truth values is called \(R_0\)-algebra and is based on the residuation and negation with respect to the \(R_0\) t-norm. The paper contains a detailed presentation of the system and a full proof of the strong completeness theorem. The last part presents the schematic extension of this system when confining to finite \(R_0\)-algebra of truth values. Again, strong completeness is proved.
scientific article; zbMATH DE number 1917788