First-Order Modal Logic
First-Order Modal Logic
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DOI：
10.1007/978-94-011-5292-1
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发表时间：
1998-10
期刊：
影响因子：
--
通讯作者：
M. Fitting;Richard L. Mendelsohn
中科院分区：
文献类型：
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作者：
M. Fitting;Richard L. Mendelsohn
在经历了二十世纪上半叶的坎坷开局之后，模态逻辑在下半叶大踏步前进。世纪中叶前后，可能世界语义学的引入使情况有所不同。可能世界语义学提供了一种具有直观吸引力的技术手段，几乎在一夜之间，这个主题变成了人们认为他们理解的东西，无论是对的还是错的。今天有很多关于模态逻辑的书。但除了少数例外，处理几乎完全是命题模式逻辑。到目前为止，这是一个工作得很好的领域，也是哲学培训的标准部分。另一方面，一阶模态逻辑在文献中没有得到充分的描述。它不是简单的命题模态逻辑加量词。出现了经典逻辑中没有的复杂情况。结果是细致入微的，富有表现力。这就是这本书的主题。为了使我们的书自成一体，我们为那些需要它的人加入了一个复读器，关于经典命题逻辑的公理和Tableau系统，以及关于可靠性和完整性的详细证明。然后，我们继续讨论模式逻辑。我们从命题模态逻辑开始，我们在这里的陈述是整本书的典型。我们的基本方法是语义学，使用可能世界或克里普克模型。证明-从理论上讲，我们的主要机制是语义表，它很容易和直观地使用。我们也包括对命题公理系统的处理，尽管公理不会贯穿整本书。在哲学上，我们讨论了激发形式化模式逻辑的问题，并考虑了技术发展对众所周知的哲学问题的影响。这种三管齐下的方法，克里普克语义学，场景和哲学讨论，随着每个新主题的引入而重新出现。传统上，一阶问题，如常量和函数符号、等式、量化和确定描述，都有直截了当的形式处理，这些都是长期以来的标准项目。从形态上讲，上述每一项都需要重新考虑。如上所述，一阶模态逻辑，最明确的是，不仅仅是命题模态逻辑加上经典的量词机器。情况比第七阶段要微妙得多。
After a rocky start in the first half of the twentieth century, modal logic hit its stride in the second half. The introduction of possible world semantics around the midcentury mark made the difference. Possible world semantics provided a technical device with intuitive appeal, and almost overnight the subject became something people felt they understood, rightly or wrongly. Today there are many books that deal with modal logic. But with only a small number of exceptions, treatments are almost entirely of propositional modal logic. By now this is a well-worked area and a standard part of philosophical training. First-order modal logic, on the other hand, is under-represented in the literature. It is not simply propositional modal logic plus quantifiers. Complications arise that have no counterpart in classical logic. The results are nuanced and expressive. That is what this book is about. To make our book self-contained, we incorporate a refresher for those who need it, on classical propositional logic both axiomatically and with tableau systems, and with detailed proofs of soundness and completeness. Then we move on to modal logics. We begin with propositional modal logic, and our presentation here is typical of the entire book. Our basic approach is semantic, using possible world, or Kripke, models. Proof-theoretically, our primary machinery is semantic tableaus, which are easy and intuitive to use. We also include a treatment of propositional axiom systems, though axiomatics do not continue throughout the book. Philosophically, we discuss the issues that motivate formal modal logics and consider what bearing technical developments have on well-known philosophical problems. This three-pronged approach, Kripke semantics, tableaus, and philosophical discussion, reappears as each new topic is introduced. Classically, first-order issues like constant and function symbols, equality, quantification, and definite descriptions, have straightforward formal treatments that have been standard items for a long time. Modally, each of these items needs rethinking. As noted above, first-order modal logic, most decidedly, is not just propositional modal logic plus classical quantifier machinery. The situation is much subtler than vii