Craig interpolation for networks of sentences

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• 作者：H. Jerome Keisler^a ; ^{keisler@math.wisc.edu} ; Jeffrey M. Keisler^b ; ^{jeff.keisler@umb.edu}
• 关键词：03B10 ; 03C40 ; 03F07 ; 68T15
• 刊名：Annals of Pure and Applied Logic
• 出版年：2012
• 期刊代码：4_01680072
• 类别：cp
• 出版时间：September, 2012
• 卷：163
• 期：9
• 页码：1322-1344
• 文件大小：324 K

摘要

The Craig Interpolation Theorem can be viewed as saying that in first order logic, two agents who can only communicate in their common language can cooperate in building proofs. We obtain generalizations of the Craig Interpolation Theorem for finite sets of agents with the following properties. (1) The agents are vertices of a directed graph. (2) The agents have knowledge bases with overlapping signatures. (3) The agents can only communicate by sending to neighboring agents sentences that they know and that are in the common language of the two agents.