无限值逻辑
在邏輯中,無限值邏輯(無限多值邏輯)是一種多值邏輯,其中真值包含連續範圍。傳統上,在亞里斯多德的邏輯中,除二值邏輯之外的邏輯都是不正常的,因為排中律排除了任何命題的兩個以上可能值(即“真”和“假”)[1]。現代三值邏輯允許額外的可能真值(即「未定」)[2],並且是有限值邏輯的一個範例,其中真值是離散的,而不是連續的。無限值邏輯則包括連續模糊邏輯,儘管某些形式的模糊邏輯可以進一步包含有限值邏輯。例如,有限值邏輯可以應用於布林值建模[3][4]、 描述邏輯[5]、和對模糊邏輯的去模糊化[6][7]。
參考資料
- ^ Weisstein, Eric. Law of the Excluded Middle. MathWorld--A Wolfram Web Resource. 2018.
- ^ Weisstein, Eric. Three-Valued Logic. MathWorld--A Wolfram Web Resource. 2018.
- ^ Klawltter, Warren A. Boolean values for fuzzy sets. Theses and Dissertations, paper 2025 (学位论文) (Lehigh Preserve). 1976.
- ^ Perović, Aleksandar. Fuzzy Sets – a Boolean Valued Approach (PDF). 4th Serbian-Hungarian Joint Symposium on Intelligent Systems. Conferences and Symposia @ Óbuda University. 2006.
- ^ Cerami, Marco; García-Cerdaña, Àngel; Esteva, Frances. On finitely-valued Fuzzy Description Logics. International Journal of Approximate Reasoning. 2014, 55 (9): 1890–1916. doi:10.1016/j.ijar.2013.09.021 . hdl:10261/131932.
- ^ Schockaert, Steven; Janssen, Jeroen; Vermeir, Dirk. Satisfiability Checking in Łukasiewicz Logic as Finite Constraint Satisfaction. Journal of Automated Reasoning. 2012, 49 (4): 493–550. doi:10.1007/s10817-011-9227-0.
- ^ 1.4.4 Defuzzification (PDF). Fuzzy Logic. Swiss Federal Institute of Technology Zurich: 4. 2014 [2018-05-16]. (原始内容 (PDF)存档于2009-07-09).