The Axes of Abstraction
summary
Claim: formal concept analysis finds the places where extent equals intent so abstractions and generalizations converge, turning ad hoc subtype debates into deterministic hierarchies. Concrete tools: boolean incidence matrices, closure operators, the concept lattice (examples show canal and channel collapsing to the same concept), extensions to fuzzy and multiset variants, and a categorical link to profunctor nuclei. Result: mining concepts from data yields reproducible abstractions that expose what assumptions are actually used and thus shrink the space of implementation choices.
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chapters (8)
- 0:00Start
- 6:20Quaternion
- 9:08Tropical Rings Selectivity
- 9:46Longevity
- 18:24Equivalence Relation
- 26:40Freeness
- 35:24Concept Lattice
- 45:05Ladder of Functional Programming
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