Abstract Traditional logic and logic programming languages cannot handle uncertainty. Fuzzy logic can, but nobody has yet devised a readily computable form. One possible way to achieve this is to define a propositional fuzzy logic, extend this to a 1st-order form, convert it to Horn-clause form, and, finally, to devise a theorem prover to manipulate the Horn clauses. The authors of the paper have already achieved the first step. The paper formally develops the second step, namely a type of 1st-order fuzzy logic that incorporates a complete set of quantifiers, qualifiers and modifiers. The fuzzy entities that represent the language are described, and a 1st-order theory is introduced that consists of an alphabet, a syntax and a set of semantics for the language.