Document Type


Publication Date

September 2012


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.


This is a preliminary version of the paper. The final version of the paper should be cited as follows: Craig interpolation for networks of sentences, H. Keisler & J. Keisler, Annals of Pure and Applied Logic 163(9), September 2012, pp.1322-1344 The full text is available at the following link:


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