Deduction Theorem for Many‐Valued Inference

In [I], PAVELKA introduced many-valued rules of inference, proposed the concept of fuzzy syntax on an abstract set, and developed a general framework for approximate reasoning. In this paper, we attemp to establish deduction theorem for many-valued inference. For simplicity, we adopt the terminology and notation in [I] without any explanation. In the sequel, assume that F is endowed with a binary operation +. Defin i t ion 1. A binary L-rule d of inference on F is called a detachment rule (with evaluation component d") if Dd' = {( x, x + y ) 1 x, y E F } , d'(x, x -+ y ) = y ( x , y E F ) .