non-logical connective: to be in a (nontrivial) superposition of (states); mixture
Schrödinger's cat is not 'dead and alive' nor is it 'dead and alive'; so long as its wavefunction does not collapse, it is in a (linear) nontrivial superposition of the states 'dead' and 'alive'. In a sense, it is in both but also neither. Likewise, someone travelling northwestward is not travelling (due) northward AND (due) westward, nor are they travelling (due) northward OR (due) westward; they are travelling a mixture of both. It can also be used for answering "yes"/"no" questions; it may or may noy be helpful in this role, but it is distinct from an elliptical or non-definitive answer. Waves especially work well with superpositions. The only decent way to denote this concept in English without resorting to long-winded roundabout descriptions is '+'.