Weak associative micanorm-based logics: [ 0, e ]-continuous ν -weak-associative logics
Eunsuk Yang · Logic Journal of IGPL · 2025
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 $ u $-weak-associative uninorm ($ u $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 $ u $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.