论文标题
FOML的捆绑额是好的交易吗?
Are Bundles Good Deals for FOML?
论文作者
论文摘要
捆绑产品通常会作为客户提供优惠。当我们将一阶模态逻辑(FOML)将量子和模式捆绑在一起(如$ \存在x \ box $,$ \ diamond \ forall x $等)时,我们得到了新的逻辑运算符,它们的组合会产生有趣的FOML片段,而无需对preticaties的数量,或模态瞄准器的数量,而无需任何限制。众所周知,找到FOML的可决定片段很难,因此我们可能会问:利用FOML的明显表现力的捆绑片段在平衡表达和复杂性方面构成了良好的交易?一些特定片段有一些积极的早期结果。在本文中,我们试图完全绘制(UN)可判决性中FOML捆绑片段的地形,在没有明确答案的情况下,我们表明它们缺乏有限的模型属性。此外,无论是在恒定域(跨州/世界)上解释逻辑还是增加域都会提出另一层复杂性。我们还提出了\ textIt {松散捆绑的片段},该片段概括了捆绑包,但保留了可决定性(超过增加的域模型)。
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).