Bundled products are often offered as good deals to customers. When we bundle quantifiers and modalities together (as in $\exists x \Box$, $\Diamond \forall x$ etc.) in first-order modal logic (FOML), we get new logical operators whose combinations produce interesting fragments of FOML without any restriction on the arity of predicates, the number of variables, or the modal scope. It is well-known that finding decidable fragments of FOML is hard, so we may ask: do bundled fragments that exploit the distinct expressivity of FOML constitute good deals in balancing the expressivity and complexity? There are a few positive earlier results on some particular fragments. In this paper, we try to fully map the terrain of bundled fragments of FOML in (un)decidability, and in the cases without a definite answer yet, we show that they lack the finite model property. Moreover, whether the logics are interpreted over constant domains (across states/worlds) or increasing domains presents another layer of complexity. We also present the \textit{loosely bundled fragment}, which generalizes the bundles and yet retain decidability (over increasing domain models).

翻译：捆绑的产品通常作为对客户的好交易而提供。 当我们以一阶模式逻辑(FOML ) 将量化和模式(如 $\ expents x\ Box$, $\ Diamond\ forall x$ et.) 组合产生FOML有趣碎片的新的逻辑操作员, 他们的组合不限制上游、 变量数量或模式范围的精确度, 众所周知, 找到FOML 的可变碎片是很难的, 因此我们可能会问 : 利用FOML 的明显直观性构成平衡直观性和复杂性的良好交易的捆绑碎片? 某些特定的碎片早期结果很少。 在本文中, 我们试图完全绘制FOML 捆绑碎片的地形, 但不限制上游、 变量数量或模型范围的精确度。 此外, 逻辑是否被解读为常态域( 跨州/ 世界) 或日益增大的域系另一个复杂层次。 我们还展示了FOML( 缩缩缩略度 ) 模式。