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Basic Semilinear Logics Based on [0, 𝑢]-continuous Uwa-uninorms
Eunsuk Yang
This paper introduces micanorm-based logics satisfying three forms of weak associativity as a weak associative generalization of the [0, 1)-continuous uninorm-based logic BUL introduced by Gabbay and Metcalfe. To be more precise, we first introduce the basic uwa-uninorm logic WA𝑈BUL and its axiomatic extensions A𝑈BUL, SA𝑈BUL as 𝑢-weak-associative uninorm analogues of the basic uninorm logic BUL. We then deal with algebraic completeness results for them by introducing their corresponding algebraic structures. Next, we introduce uwauninorms as uninorms satisfying weak u-associativity in place of associativity and study related algebraic properties.We finally show that the uwa-uninorm logics are standard complete, that is, complete on unit interval [0, 1], using Yang–style construction.
Keywords: Fuzzy logic, t-norm, uwa-uninorm, uninorm, micanorm