
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.
Mathematical logic, Discrete mathematics
Mathematical logic, Discrete mathematics
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