The IFF Approach to the Lattice of Theories
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The IFF approach for the notion of "lattice of theories" uses the idea of a concept lattice from Formal Concept Analysis (Ganter and Wille) and the idea of the truth classification from Information Flow (Barwise and Seligman). The IFF approach is concentrated in the joining of these two important ideas. The result is called the truth concept lattice, the concept lattice of the truth classification. The IFF provides a principled (versus ad hoc) approach for John Sowa's "lattice of theories" framework. The "lattice of theories" is represented by the truth concept lattice, each theory in the lattice is represented by a formal concept in the truth concept lattice.
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