lakatos-heuristics

name	lakatos-heuristics
description	Proofs and Refutations method: generate counterexamples, attempt monster-barring, incorporate surviving counterexamples as lemma refinements.
type	strategy
dependencies	{"tactics":["contradiction-derivation","counterexample-heuristics"],"sops":["claim-refinement","contradiction-detection","counterexample-generation","monster-barring-attempt"]}

Lakatos Heuristics

Tactics

• counterexample-heuristics
• contradiction-derivation

Method

1. Take the claim as a tentative theorem
2. Generate counterexamples systematically
3. For each counterexample, attempt monster-barring (exclude as illegitimate)
4. If monster-barring fails, incorporate as lemma (refine the claim)
5. Iterate until claim is robust or abandoned

Budget

Size	Counterexamples	Monster-barring rounds	Lemma incorporations
S	5	2	2
M	12	4	4
L	25	8	8

Orchestration

1. Dispatch counterexample-generation against the claim
2. For each counterexample, dispatch monster-barring-attempt
3. If barring fails, dispatch claim-refinement to incorporate lemma
4. Repeat until saturation or budget exhausted

Subagents

• counterexample-generation
• monster-barring-attempt
• claim-refinement
• contradiction-detection

Available Tactics

Optional, no fixed order; the final leaf is always a sop.

Tactic	When to use
contradiction-derivation	Negate a claim, derive logical consequences step by step, detect whether a genuine contradiction or absurdity emerges.
counterexample-heuristics	Generate counterexamples (monsters), attempt monster-barring, incorporate surviving counterexamples as lemma refinements (Lakatos method).

Available SOPs

Optional, no fixed order; the final leaf is always a sop.

SOP	When to use
claim-refinement	Propose a refined claim that survives counterexamples while preserving maximum explanatory power (Lakatos lemma-incorporation).
contradiction-detection	Evaluate whether a derivation chain has reached a genuine contradiction, absurdity, or inconclusive state.
counterexample-generation	Systematically generate counterexamples (monsters) to a given claim using diverse heuristic strategies.
monster-barring-attempt	Attempt to exclude a counterexample as illegitimate by tightening definitions or preconditions (Lakatos monster-barring).