An effort to initiate the subject of the title: the basic tool is the study of the abstract closed interval equipped with certain equational structures.
Keywords: algebraic real analysis, closed interval, closed midpoint algebra, chromatic scale, coalgebraic real analysis, complete scale, finitely presented scale, free scale, harmonic scale, injective scale, lattice-ordered abelian group, linear logic, Lipschitz extension, Lukasiewicz logic, midpoint algebra, minor scale, modal logic, ordered wedge, scale, semi-simple scale, simple scale, zoom operator
2000 MSC: 03B45, 03B50, 03B70, 03D15, 03F52, 03F55, 03G20, 03G25, 03G30, 08A99, 18B25, 18B30, 18F20, 26E40, 28E99, 46M99, 34A99
Theory and Applications of Categories,
Vol. 20, 2008,
No. 10, pp 215-306.
http://www.tac.mta.ca/tac/volumes/20/10/20-10.dvi
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http://www.tac.mta.ca/tac/volumes/20/10/20-10.pdf
ftp://ftp.tac.mta.ca/pub/tac/html/volumes/20/10/20-10.dvi
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