Fuzzy logic and arithmetical hierarchy III

被引:18
作者
Hájek P. [1 ]
机构
[1] Institute of Computer Science, Academy of Sciences of the Czech Republic, 2 182 07 Prague, Pod Vodárenskou Věží
关键词
Arithmetical hierarchy; Basic fuzzy logic; Fuzzy logic; Gödel logic; Product logic; ŁUkasiewicz logic;
D O I
10.1023/A:1011906423560
中图分类号
学科分类号
摘要
Fuzzy logic is understood as a logic with a comparative and truth-functional notion of truth. Arithmetical complexity of sets of tautologies (identically true sentences) and satisfiable sentences (sentences true in at least one interpretation) as well of sets of provable formulas of the most important systems of fuzzy predicate logic is determined or at least estimated. © 2001 Kluwer Academic Publishers.
引用
收藏
页码:129 / 142
页数:13
相关论文
共 15 条
  • [1] Baaz M., Infinite-valued Gödel logics with 0-1 projections and relativization, Gödel'96, pp. 23-33, (1996)
  • [2] Baaz M., Hajek P., Montagna F., Veith H., Complexity of t-tautologies, Annals of Pure and Applied Logic
  • [3] Cignoli R., D'ottaviano I.M.L., Mundici D., Algebraic Foundations of Many-valued Reasoning, (2000)
  • [4] Cignoli R., Esteva F., Godo L., Torrens A., Basic fuzzy logic is the logic of continuous t-norms and their residua, Soft Computing, 4, pp. 106-112, (2000)
  • [5] Esteva F., Godo L., Hajek P., Navara M., Residuated logics with an involutive negation, Arch. Math. Logic
  • [6] Esteva F., Godo L., Montagna F., The ŁΠ and ŁΠ 1/2 logics: Two complete systems joining Łukasiewicz and product logic, Arch. Math. Logic
  • [7] Hajek P., Fuzzy logic and arithmetical hierarchy, Fuzzy Sets and Systems, 73, 3, pp. 359-363, (1995)
  • [8] Hajek P., Fuzzy logic and arithmetical hierarchy IP, Studia Logica, 58, pp. 129-141, (1997)
  • [9] Hajek P., Metamathematics of Fuzzy Logic, (1998)
  • [10] Hajek P., Mathematical fuzzy logic - State of art, Proc. Logic Colloquium'98, (2000)