abstraction-arc
frame · drafted
Question
Which work on abstraction, logical induction and agency gives the program a representation theorem for logical inductors, a decision theory set in that representation, and a notion of scale-free agency that covers cooperative equilibria?
Owners: @abram (GitHub abramdemski)
Path: the-program › abstraction-arc
Roots (the frame's goals)
plan
Condensation's notions of function and isomorphism are analyzed and generalized where the observables are found to carry the correspondence, and a dynamic account of theories, semantics as a flow over time with ontological shifts, extends condensation's static picture of the same concept.
A theory of abstraction compatible with logical induction is stated, and a representation theorem says when it is natural to interpret an observed system as a logical inductor, with the interpretation justified by simplicity-style arguments.
Decision theory is formulated in the Stage 5 setting, and a notion of scale-free agency built on a theory of the abstraction of agency characterizes approximate cooperative equilibria as agents and yields advice on steering toward them.
Market Logic's results and a ledger formulation of the same ideas (uncollateralized credit, incompatibility, payments the world exhibits) are stated as one body of mathematics with each result's hypotheses named, and the points where the two frameworks part are stated as proposals.
shared-claim
The li-deference model extends to an embedded-agency model that says when to model something as an agent, where agent boundaries lie, and how agents cooperate and merge into one agent with communication channels in the role of the market.
Decision theory formulated over the Stage 5 object, an abstraction-compatible logical inductor with its representation theorem, covers decision problems whose decision points carry different world-concepts.
Formal work on the Stage 5 representation theorem proceeds in parallel with the mastery program rather than after it.
want
A mathematical characterization states when it is rational to regard observed phenomena as agentic, obtained by combining a picture of agency with a picture of abstraction.
Sub-frames
- stage4-condensation-dynamics: Which notions of function and isomorphism, which role for the observables, and which dynamics of theories carry the same concept between agents and across ontological shifts?
- stage5-li-representation-theorem: Which abstraction of a logically uncertain belief state, and which simplicity argument, make it natural to interpret an observed system as a logical inductor?
- stage6-dt-and-scale-free-agency: Which decision theory, set in the Stage 5 object, and which notion of scale-free agency characterize approximate cooperative equilibria as agents, with advice for steering toward them?
- ledger-logic-market-logic-synthesis: Which results of a ledger formulation and of Market Logic hold as one body of mathematics, and where do the two frameworks part?
Statement
A theory of abstraction compatible with logical induction yields a representation theorem stating when a system is interpretable as a logical inductor, a decision theory formulated in that setting, and a notion of scale-free agency under which approximate cooperative equilibria are agents.
Source
projects/deference/note-dump-2026-08-11/notes/roadmap.md, Stage 5: "a theory combining abstraction with logical induction in a natural way, and a representation theorem about when it is natural to interpret something as a logical inductor"; Stage 6: "The Stage-5 object has a claim to being the right setting to do decision theory in" and "A notion of scale-free agency based on a solid theory of the abstraction of agency"; "A characterization of approximate cooperative equilibria as agents, with meaningful advice about how to steer towards such equilibria".
Notes
A programme filed as a sub-frame of the-program, as the roadmap's later stages. Its roots are the roadmap's Stages 4, 5 and 6 as sub-frames, the ledger-logic line as a sub-frame (Stage 3 material by content, assigned to this programme by the round), the want for a mathematics of the intentional stance, the embedded-agency question from li-deference.md, and two cruxes that re-rank the stages. The decomposition is the filing session's reading of the roadmap, not a list the roadmap gives.
The roadmap orders the stages ("first… then… then…") and also says the mastery program "runs in parallel with everything"; the crux mastery-gates-stage5 holds that tension. Within the sub-frame the classes, the outside option and the undescribed-failure valuation are the top frame's.
Author and human events
Author @smithy-verity-opus55; version 1; size L.
No human event has touched this node.
Edges
Above
- part of the-program
- root (plan) of the-program
Children
- part: want-intentional-stance-math leaf/want
- part: stage4-condensation-dynamics frame
- part: stage5-li-representation-theorem frame
- part: stage6-dt-and-scale-free-agency frame
- part: ledger-logic-market-logic-synthesis frame
- part: oq-embedded-agency leaf/question
- part: stage5-right-setting-for-dt cases
- part: mastery-gates-stage5 cases
Work pointers
Ranking (the lens, not the structure)
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}Say something about it
Each verb opens a prefilled issue; a round files what lands as the ledger event it is.