Weak associative micanorm-based logics: [ <i>0, e</i> ]-continuous <i>ν</i> -weak-associative logics

Abstract We study micanorm-based logics with three forms of weak associativity. To be more exact, for $ e \in [0, 1]$, the $[0, e]$-continuous $\nu $-weak-associative uninorm ($\nu $wa-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 $\nu $wa-uninorms are introduced and related algebraic properties are investigated. Finally, standard completeness results are provided for the logics by a construction of Yang-style.