A syntactical approach to modality
A syntactical approach to modality
复制标题
情态的句法方法
DOI：
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发表时间：
1992
影响因子：
1.5
通讯作者：
P. Schweizer
中科院分区：
文献类型：
--
作者：
P. Schweizer
结论TN和TM系统表明，如果系统的表达/演绎能力被刻意设计成反映原始对象语言算子的能力，必然性可以被一致地解释为句法对象的谓词。系统TN依赖于通过构建引用层次结构对语言LN的表达能力的显著限制，而系统TM依赖于将模态公理模式的范围限制到子语言LinfM+，这与LN的限制性层次结构完全对应。LinfM+与C+从正常算子系统到LM的元语言映射的图像相同的事实表明，迭代算子模态是隐式分层的，并且不一致性是通过将模态逻辑的原理应用于在算子发展中没有自然类似物的公式而产生的。因此，蒙塔古发现的矛盾可以被诊断为用模态无基公式实例化公理模式的结果，从而为谓词系统添加了全新的模态公理。谓词对必然性的处理与算子的处理有很大的不同，因为谓词系统的累积模型是严格的一阶模型。可能的世界不被用作模型理论的原语，而是呼吁替代模型，以指定N的扩展，这是语义上解释为一阶谓词。以这种方式，模态的内涵方面被构建到指定指称函数分配给N的特定对象集合的模式中，而不是在模态公式的基本真值条件的规范中。因此，内涵现象被局限于确定特定谓词的外延的特殊要求，这并不构成一阶模型的结构修改，而是将相关的模型类别限制为具有适当指称功能的模型。
ConclusionThe systems TN and TM show that necessity can be consistently construed as a predicate of syntactical objects, if the expressive/deductive power of the system is deliberately engineered to reflect the power of the original object language operator. The system TN relies on salient limitations on the expressive power of the language LN through the construction of a quotational hierarchy, while the system TMrelies on limiting the scope of the modal axioms schemas to the sublanguage LinfM+, which corresponds exactly with the restrictive hierarchy of LN. The fact that LinfM+ is identical to the image of the metalinguistic mapping C+ from the normal operator system into LM reveals that iterated operator modality is implicitly hierarchical, and that inconsistency is produced by applying the principles of the modal logic to formulas which have no natural analogues in the operator development. Thus the contradiction discovered by Montague can be diagnosed as the result of instantiating the axiom schemas with modally ungrounded formulas, and thereby adding radically new modal axioms to the predicate system.The predicate treatment of necessity differs significantly from that of the operator in that the cumulative models for the predicate system are strictly first-order. Possible worlds are not used as model-theoretic primitives, but rather alternate models are appealed to in order to specify the extension of N, which is semantically construed as a first-order predicate. In this manner, the intensional aspects of modality are built into the mode of specifying the particular set of objects which the denotation function assigns to N, rather than in the specification of the basic truth conditions for modal formulas. Intensional phenomena are thereby localised to the special requirements for determining the extension of a particular predicate, and this does not constitute a structural modification of the first-order models, but rather limits the relevant class of models to those which possess an appropriate denotation function.