Weak associative micanorm-based logics: [0, e]-continuous ν-weak-associative logics

We study micanorm-based logics with three forms of weak associativity. To be more exact, for e ∈ [0, 1], the [0, e]-continuous v-weak-associative uninorm (vwa-uninorm) logics tuWABUL, tuABUL, and tuSABUL are first introduced as a weak associative generalization of BUL (Basic uninorm logic). Their algebraic semantics and completeness results are then addressed. Next, [0, e]-continuous vwa-uninorms are introduced and related algebraic properties are investigated. Finally, standard completeness results are provided for the logics by a construction of Yang-style.