Standard Completeness for the Weak Uninorm Mingle Logic WUML

WUML의 표준적 완전성

Fixed-point conjunctive left-continuous idempotent uninorms have been introduced (see e.g. [2, 3]). This paper studies a system for such uninorms. More exactly, one system obtainable from IUML (Involutive uninorm mingle logic) by dropping involution (INV), called here WUML (Weak Uninorm Mingle Logic), is first introduced. This is the system of fixed-point conjunctive left-continuous idempotent uninorms and their residua with weak negation. Algebraic structures corresponding to the system, i.e., WUML-algebras, are then defined, and algebraic completeness is provided for the system. Standard completeness is further established for WUML and IUML in an analogy to that of WNM (Weak nilpotent minimum logic) and NM (Nilpotent minimum logic) in [4].

이 논문은 uninorm의 한 체계인 WUML(Weak Uninorm Mingle Logic)을 다룬다. 먼저 WUML을 도입하고, 그 체계에 상응하는 대수적 구조를 정의한다. 그런 다음 그 체계의 대수적 완전성을 증명한다. 끝으로 WUML과 IUML의 표준적 완전성을 증명한다.