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How does the IFF represent the lattice of theories?

April 26, 2017iff Lattice theories

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How does the IFF represent the lattice of theories?

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The IFF representation for the lattice of theories is called the truth concept lattice. The truth concept lattice is equivalent to the truth classification. See the illustration on slides 5 and 6 of the SUO Workshop PowerPoint presentation. The truth classification was discussed as example 4.6 on page 71 of the book Information Flow: The Logic of Distributed Systems by Jon Barwise and Jerry Seligman. The truth concept lattice is introduced for the first time here in the SUO IFF. An element of the truth concept lattice, called a truth formal concept, is a closed theory.