The IFF Approach to the Lattice of Theories

TL;DR

The paper introduces the IFF approach, combining Formal Concept Analysis and Information Flow to formalize the lattice of theories as a truth concept lattice, providing a principled framework for representing theories.

Contribution

It presents a novel formalization of the lattice of theories using the truth concept lattice, integrating two foundational ideas for a more rigorous approach.

Findings

Defines the truth concept lattice as a formal structure.

Shows how theories correspond to formal concepts.

Provides a principled framework for the lattice of theories.

Abstract

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.