Deductive Strategy Discovery

Input: $ARGUMENTS

Overview

Derive strategies by working backward from success criteria to required actions. Instead of brainstorming “what could work?” this procedure asks: “What MUST be done to satisfy the problem axioms?”

The output is strategies with explicit logical derivations showing WHY they are necessary, not just possible.

Steps

Step 1: Extract Problem Axioms

Convert the problem/goal into formal axioms:

Success criteria (what must be true when done):

S1: [condition that must hold]
S2: [condition that must hold]

Constraints (what cannot be violated):

C1: [limitation]
C2: [limitation]

Givens (facts about the current situation):

G1: [what’s true now]
G2: [what’s true now]

Quality check: Are the axioms complete? Ask: “If all success criteria are met and no constraints are violated, is the goal achieved?” If not, axioms are incomplete.

Step 2: Derive Necessary Requirements

From each success criterion, work backward:

S1 requires: [what must be done to make S1 true]
  which requires: [predecessor condition]
    which requires: [predecessor condition]
      ...until you reach something you can DO

For each requirement chain:

Is this requirement NECESSARY (can’t achieve S without it)?
Or just SUFFICIENT (one way to achieve S, but not the only way)?
Mark each: [NECESSARY] or [SUFFICIENT]

Step 3: Identify Strategy Space

From the requirement chains, map the choice points:

STRATEGY SPACE:
To achieve S1:
  Path A: [requirement chain A] — NECESSARY
  Path B: [requirement chain B] — SUFFICIENT (alternative exists)
    Alternative B1: [variant]
    Alternative B2: [variant]

Where chains are NECESSARY: no choice — must do it. Where chains have alternatives: these are strategy choice points.

Step 4: Apply Elimination Reasoning

For each choice point, eliminate options:

Does option violate any constraint? → ELIMINATE
Does option require a resource not available? → ELIMINATE (or flag for /cnw)
Does option conflict with another necessary requirement? → ELIMINATE
Does option have strictly lower merit than another on all dimensions? → ELIMINATE (dominated)

After elimination: what remains?

One option → Strategy is determined
Multiple options → Need evaluation (/dse)
No options → Problem may be infeasible — revisit axioms

Step 5: Build Strategy Proofs

For each surviving strategy, construct the full proof:

STRATEGY PROOF:
Theorem: Strategy [X] achieves goal [G]

Proof:
1. Goal requires S1, S2, S3 [by definition]
2. S1 requires R1 [derived in Step 2]
3. R1 is achieved by action A1 [only viable option after elimination]
4. S2 requires R2 [derived in Step 2]
5. R2 is achieved by action A2 [chosen from alternatives because...]
6. S3 requires R3 [derived in Step 2]
7. R3 is achieved by action A3 [necessary — no alternative]
8. A1, A2, A3 do not violate C1, C2 [checked in Step 4]
9. Therefore: Strategy {A1, A2, A3} achieves {S1, S2, S3} ∎

Proof strength: [NECESSARY / SUFFICIENT / CONTINGENT]
Key assumption: [weakest link in the proof]

Step 6: Classify Strategy Confidence

Level	Criteria	Meaning
Proven necessary	All steps are necessary, all premises verified	Only possible strategy
Proven sufficient	Steps will achieve goal, premises verified	Will work, but alternatives exist
Contingent	Steps will achieve goal IF assumptions hold	Depends on untested assumptions
Plausible	Reasoning is sound but premises are uncertain	Probably works
Speculative	Significant gaps in reasoning	Might work

Step 7: Report

DEDUCTIVE STRATEGY DISCOVERY:
Goal: [what]
Axioms: [N] success criteria, [N] constraints, [N] givens

Derivation:
[Key reasoning steps]

Strategy: [the derived approach]
Proof strength: [level]
Key assumption: [weakest link]

Necessary actions: [things that MUST be done regardless of strategy choice]
Choice points: [where alternatives exist]
Eliminated options: [what was ruled out and why]

Confidence: [level with justification]
What would upgrade confidence: [what evidence/test would help]

When to Use

At the start of strategy discovery
When existing strategies feel like “guesses”
When you want strategies that feel self-evidently correct
When you need high confidence before committing resources
→ INVOKE: /dse (deductive strategy evaluation) for evaluating derived strategies
→ INVOKE: /lps (logical proof system) for formal proof infrastructure
→ INVOKE: /dari (deductive adversarial review integration) for adversarial testing

Verification

All success criteria traced to required actions
Constraints checked against all strategies
Necessity vs sufficiency explicitly stated for each requirement
Critical assumptions identified
At least one strategy has proof strength of SUFFICIENT or higher

dsd