相干逻辑关系语义的推理解释  

An Explanation for the Relational Semantics of Relevance Logic

作　　者：周北海[1] 贾青[2] 

机构地区：[1]北京大学哲学系 [2]中国社会科学院哲学研究所

出　　处：《逻辑学研究》2015年第1期50-64,共15页Studies in Logic

基　　金：国家社科基金重大项目(批准号12&ZD119)

摘　　要：关系语义是相干逻辑中最为重要的语义学之一,但是关系语义一开始就以"纯粹"的形式语义的面貌出现,其中三元关系R的直观意思是什么并不清楚,于是出现了关于关系语义的多种解释。我们认为,R所代表的是推理规则集、前提集和结论集三者之间的关系,据此提出了推理语义。推理语义以推理的形式结构为背景,有明确的直观意义。本文以相干逻辑系统R+为例,证明出推理语义是与关系语义等价的语义。从推理语义与关系语义的这个等价关系上看,推理语义完全可以作为对于关系语义直观解释的一个中间环节。由此不仅使得关系语义有了推理结构的解释,同时说明了相干逻辑是一种关于推理的逻辑。这与相干逻辑产生的历史也完全吻合。Relational semantics is one of the most popular semantics for relevance logic. How- ever, because this semantics is a kind of＂purely＂ formal semantics, the ternary relation R lacks intuition, and that is why there are various interpretations for relational seman- tics. As to our opinion, R is a representation of the relation among rules, premises and conclusions. Based on this opinion, inference semantics is presented. The background of inference semantics is the formal structure of inference and this feature makes inference semantics intuitive for our understanding. In this paper, we will prove that relational semantics and inference semantics are equivalent with respect to the relevance logical system R＋. From this equivalence relation, inference semantics could be viewed as an intermediate link for the intuitive interpretation of relational semantics. By inference semantics, relational semantics could got an interpretation from the structure of infer- ence. Relevance logic is a logic of inference, so inference semantics is coincident with the history of relevance logic.

关 键 词：相干逻辑 关系语义 推理语义 

分 类 号：B81[哲学宗教—逻辑学]