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Deduction Theorem for Many‐Valued Inference
Author(s) -
Ying Mingsheng
Publication year - 1991
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.19910373304
Subject(s) - inference , citation , china , mathematics , link (geometry) , calculus (dental) , mathematical economics , mathematics education , computer science , library science , combinatorics , artificial intelligence , political science , law , medicine , dentistry
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 ) .