Mathematics Operations Research From Rs Ormethod

The five methods

Operations research is the discipline of using mathematical models to support decisions, and its textbooks usually organize the field into a handful of standard toolkits. The most common list names five: linear programming, dynamic programming, game theory, queuing theory, and simulation. The Recognition Science framework's machine-checked library of formal theorems contains a declaration, ORMethod, that does exactly one thing: it defines these five as the complete set of canonical methods. A companion theorem proves that the count is five, and the proof is a direct computation that the library checks without any unproved assumptions.

The declaration also connects this list to the framework's core idea of recognition cost, which is a number the framework assigns to how hard it is to recognize a state of affairs. In this account, optimization is modeled as choosing the decision that minimizes that cost, and the minimum possible cost is zero. A second theorem in the same file proves that the cost function reaches zero when its input is exactly one, written as Jcost 1 = 0. The two results, the count of five and the zero minimum, are packaged together in a single structure called an operations research certificate.

What the declaration does not do is more important than what it does. It does not claim that these five methods are the only possible ways to do operations research, nor that they are the best ones. It does not prove that any real optimization problem has a solution, or that minimizing the framework's cost function matches what a human decision maker would want. The count of five is a definitional choice, a way of carving the field that the framework adopts, and the zero-cost theorem is a statement about the framework's own cost function, not about the difficulty of actual decisions. The declaration is a small piece of bookkeeping, a labeled container that says: these five, and no more, are the canonical methods in this framework.

inductive ORMethod where
  | linearProgramming | dynamicProgramming | gameTheory | queuingTheory | simulation
  deriving DecidableEq, Repr, BEq, Fintype

theorem orMethodCount : Fintype.card ORMethod = 5 := by decide

/-- Optimal solution: J = 0. -/
theorem optimal_solution : Jcost 1 = 0 := Jcost_unit0

What this page does not claim

The declaration does not claim these five methods are the only possible or the best methods in operations research. The zero-cost theorem does not claim that any real decision problem has a solution or that minimizing J matches human preferences. The count of five is a definitional choice, not a derived necessity.

Verify this page

Every tagged claim above names its theorem. To check one yourself rather than trust this page, elaborate the source module with Lean 4 and audit its axiom basis:

$ lake env lean IndisputableMonolith/Mathematics/OperationsResearchFromRS.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

A page whose claims cannot be reproduced this way does not ship. In production, every anchor links to the exact declaration in the public source release, and this block carries the build receipt for the page itself.

Derived articles

This page is generated by a question-recursion engine: the questions its answers raise become the next pages. The current agenda, with open targets marked red: