Composition and Transformation
In Binary Logic, the “value” of a relation is only 0 or 1.
This is why “school logic” can seem boring — Binary Logic only thinks in “yes or no”!
In real life, we make all kinds of connections between things.
If we’re planning a trip to the mountains, we think about more than just “can I get there” (yes or no) — we think about the set of ways to get there, or the distance, or the resources it will take.
This is the idea of Matrix Logic:
<aside> 🌟 A relation can be any predicate of a pair of types — any “thought” that depends on two “types of thing” — as long as we can define composition and identity.
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<aside> 📖 The construction of matrix logics is given in Section 14 of Framed Bicategories and Monoidal Fibrations, Shulman 2007.
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