Fuzzy unification as a foundation of fuzzy logic programming

In the development of a fuzzy logic programming language fuzzy uni cation assumes a central role Several proposals have been made to give a formal and complete de nition of this operation In this paper we propose three di erent kinds of uni cation in the fuzzy context A fuzzy uni cation algorithm is presented ex tending through similarity relations the uni cation algorithm of Martelli Montanari used in the classical case An alternative ap proach is proposed through a Quotient Uni cation based on an equivalence relation which gives rise to equivalences classes that can be used in logic programming to identify similar objects Then Uni cation as Negotiation is described based on a more exible form of uni cation with semantic constraints Finally three fuzzy resolution rules are de ned based on the corresponding kinds of fuzzy uni cation introduced