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Decision-Environment Constraint Dynamics: A Formal Specification

Authors: John Paul, Marat;

Decision-Environment Constraint Dynamics: A Formal Specification

Abstract

We introduce a formal algebraic framework for analyzing how decision environmentsbecome progressively constrained. A decision environment is a triple ⟨I, A, ℓ⟩ comprisingan information substrate, an action substrate, and a loss function ℓ : I × A → R≥0. Fourmonotone operators, Frame (F), Control (C), Obligation (O), and Sanction (S), act on thistriple by restricting information availability, contracting action feasibility, introducing inter-nal loss obligations, and imposing external loss penalties, respectively. We prove that theseoperators form a canonical accumulation ordering F → C → O → S induced by preconditiondependencies, establish multiple stabilization criteria under which the environment reachesa fixed point under the operator family, and derive minimality and non-redundancy resultsguaranteeing that the operator vocabulary is both sufficient and irreducible. The frameworkis extended to stochastic loss functions and partial-observability projections, with analogousstabilization guarantees. All constructions are substrate-independent: the definitions invokeno domain-specific, epistemic, psychological, or normative primitives.

Keywords

Mathematical logic, Discrete mathematics

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average