Our paper, "Use of Logic Relationships to Decipher Protein Network Organization", attempts to identify ternary logical relationships between phylogenetic triples of proteins. The paper and some supplementary material can be accessed here.

I'm also trying to make the algorithm available for those that would like to use it. It was supposed to show up with the supplementary materials, but it looks as the editors included only the first five supplementary docs.

Right click and save the gzipped archive below, which contains OSX and Windows C++ source code and documentation. An example input binary matrix and logical description output for PPLA is included in both the OSX and Windows folders in the extracted archive

The method seeks to identify ternary logical relationships within genomic data that are not identified by traditional pairwise analysis. A raw COG binary matrix and COG description file are available here and here.