捆绑包对FOML来说是好交易吗？
Are Bundles Good Deals for FOML?
摘要：
捆绑销售的产品往往是作为一个很好的交易提供给客户。当我们将量词和情态捆绑在一起时（如$\exists x \Box$、$\Diamond \forall x$等），在一阶模态逻辑（FOML）中，我们得到新的逻辑运算符，它们的组合产生FOML的有趣片段，而对谓词的数量、变量的数量或模态范围没有任何限制。众所周知，找到FOML的可判定片段是很困难的，所以我们可能会问：利用FOML独特表达能力的捆绑片段是否构成了平衡表达能力和复杂性的好交易？有一些积极的早期结果对一些特定的片段。在本文中，我们试图充分映射的FOML的捆绑片段的地形在（非）可判定性，并在没有一个明确的答案的情况下，我们表明，他们缺乏有限的模型属性。此外，无论逻辑是在恒定域（跨状态/世界）还是增加域上解释，都呈现出另一层复杂性。我们还提出了\textit{loosely bundled fragment}，它概括了捆绑，但保留可判定性（增加领域模型）。
英文摘要：
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).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
