Extended Fuzzy Equational Logic
We study fuzzy equational logics extended by additional deduction rules. It is shown that equational deduction rules which preserve substitutions can be represented by Horn clauses with truth-weighted premises. This ensures us to reduce provability in extended fuzzy equational logics to provability in fuzzy Horn logic. We work in Pavelka-style (we use truth-evaluated syntax) and prove Pavelka-style completeness of extended fuzzy equational logics.