Beyond Accessibility: Functional Models for Modal Logic
Beyond Accessibility: Functional Models for Modal Logic
复制标题
超越可访问性：模态逻辑的功能模型
DOI：
10.1007/978-94-015-8242-1_1
复制
发表时间：
1993
影响因子：
1.5
通讯作者：
J. Benthem
中科院分区：
文献类型：
--
作者：
J. Benthem
通过康格、辛提卡和克里普克的工作，模态逻辑的可能世界语义学在50年代得到了发展。它的主要思想是使用可能世界(可能世界在某种意义上可能代表世界，但也可能代表时间点、情境、信息阶段或计算机状态)，由可能性模式构建-每个世界中的个体对象生活在域中，并在那里具有属性，这些属性可能在从一个世界转移到另一个世界时发生变化。在命题模式逻辑中，只有世界和可访问性很重要(加上解释整个模式上的原子命题的‘估值’)，这种情况似乎总是非常明显的。但在情态谓词逻辑中，关于在语义上做出适当选择的争论一直反复存在，从Quine[25]早期对将必要属性归因于对象的一致性的怀疑开始，一直持续到六七十年代，对世界各地的个人的“跨世界身份”有不同的描述。值得注意的是刘易斯[21]的“对应理论”，它否认对象可以在不同的世界中明智地相同，或者克里普克[20]中的“严格指定”理论，它肯定只有这样的对象才有意义。在Fine[9]和Carson[13]中给出了各种可能方法的更详细的描述。因此，哲学文献展示了情态谓词逻辑的语义中的各种可能的选择，既涉及个体的本质，也涉及与个体有关的必要命题的解释。尽管如此，仍然存在一种广泛的标准观点(参见Hughes和Cresswell[17]具有沿着可访问性模式增长的域(即，当每次xRy时)，并且在当φ持有所有可访问世界中的相同对象的世界中调用关于对象d1，...，dn的语句-φ(xl，...，xn)True。
Possible worlds semantics for Modal Logic evolved in the fifties, through the work of Kanger, Hintikka and Kripke. Its main ideas are the use ofpossible worlds(which may stand for worlds in some grand sense, but also for points in time, situations, information stages or computer states), structured by a pattern ofaccessibility—with individual objectsliving in domains per world and having properties there, which may change in passing from one world to another. In propositional modal logic, where only worlds and accessibility matter (plus a ‘valuation’ for interpreting atomic propositions over the whole pattern), this picture has always seemed perfectly obvious. But in modal predicate logic, there has been recurrent debate concerning appropriate choices to be made in the semantics, starting from early doubts in Quine [25] about the very coherence of ascribing necessary properties to objects, and continuing into the sixties and seventies with various accounts of ‘trans-world identity’ for individuals across worlds. Noticeable are the ‘counterpart theory’ of Lewis [21], denying that objects can sensibly be identical across different worlds, or the ‘rigid designation’ theory in Kripke [20], affirming that only such objects make sense. More elaborate accounts of various possible approaches are given in Fine [9] and Carson [13]. Thus, the philosophical literature shows a variety of possible options in the semantics of modal predicate logic, concerning both the nature of individuals, and the interpretation of necessary propositions concerning them. Still, a widespread standard view exists (cf. Hughes and Cresswell [17] with domains growing along accessibility patterns (i.e., wheneverxRy, then), and calling a statement □φ(xl,...,xn) true of objectsd1,...,dnin a world iffφholds of those same objects in all accessible worlds.