ledger-logic-market-logic-synthesis

One criterion stands behind validity, probability, utility, decision and coordination: a rule of a ledger is justified by exhibiting the book that would be made against a ledger without it.

The market-maker of Market Logic I is the logical-induction paper's market-maker with sentences replaced by arbitrary goods, and its Fixed Point Lemma bounds the day's aggregate trade on the whole price cube without using Boolean structure.

Market Logic's market over goods can be improved until it reflects belief and logic dynamics with a proof theory well, as a computable process.

Market Logic II's turnstile, read as pointwise dominance of payoffs, is the degree-preserving Łukasiewicz relation rather than Łukasiewicz consequence; tonk is a sure loss for the maker; the two disjunctions are Girard's additive and multiplicative pair; and the shared-context rules price 'if' as Gödel's conditional.

The de Finetti Dutch-book argument run with arbitrary terminal values gives that coherent prices are the convex hull of the admissible resolutions, so the argument's classical-logic assumption is a choice of which resolutions are admissible; the Łukasiewicz instance is prior art.

Where the ledger has uncollateralized credit, incompatibility and a payment the world exhibits, the market has collateral, hedging and wealth, and an infinitely wealthy trader is an unscored page only when it is the sole settlement channel.

The standard governing prices on never-settled questions comes from a legitimacy-modified version of the logical-induction trust principles (Total Trust, the tower or Reflection), as li-deference.md places legitimacy, rather than from the market's limit.