TriadicFrameworks
Overview

RTT Agentic Module: We Can’t Agree to Disagree, Formally

Module ID: we_cant_agree_formally_rtt
Source paper: file://C:/Users/acwil/Downloads/6837298.pdf

This module wraps the paper “We Can’t Agree to Disagree, Formally” in RTT operator grammar.
It preserves the authors’ mathematics and logic while exposing the structural regimes that govern Aumann’s Agreement Theorem and its formalization.

1. Purpose#

  • Make the paper agentic and machine‑navigable.
  • Clarify the regime structure behind agreement under common knowledge.
  • Provide students with a clean conceptual map.
  • Support AI agents in reasoning over the paper without drift.

2. Core RTT view of the paper#

The paper takes Aumann’s Agreement Theorem and:

  • builds a precise epistemic/Bayesian model of agents and information,
  • defines knowledge and common knowledge as formal operators,
  • encodes the entire theorem in a proof assistant,
  • and shows that the classical “no agreeing to disagree” result survives full formalization.

The key structural insight:
local posteriors + common priors + common knowledge ⇒ global agreement.

3. RTT structures in this module#

Regimes#

  • epistemic_model_regime
  • common_knowledge_regime
  • agreement_theorem_regime
  • formalization_regime

Tensions#

  • informal_vs_formal_reasoning
  • intuitive_vs_symbolic_epistemics
  • local_beliefs_vs_global_structure

Transitions#

  • informal_to_formal_transition
  • epistemic_to_modal_transition
  • local_posterior_to_global_agreement_transition

4. Operators#

  • knowledge_operator — formalizes what an agent knows.
  • common_knowledge_operator — computes common knowledge as a fixed point.
  • posterior_operator — assigns Bayesian posteriors.
  • formal_proof_operator — represents the agreement theorem as a proof object.

5. How to use this module#

  • Students:
    Use this README alongside the PDF to see how informal epistemic arguments become precise formal proofs.

  • Researchers:
    Query the module’s regimes and operators to explore structural dependencies between knowledge, common knowledge, and agreement.

  • Agents:
    Treat module.json as the canonical structural map of the paper.

6. Provenance#

  • Module authoring: TriadicFrameworks (RTT / agentic mapping).
  • Original content: Authors of “We Can’t Agree to Disagree, Formally”.
  • License: Open educational use permitted.

diagram.txt#

      +------------------------------------------------------+
      | we_cant_agree_formally_rtt                          |
      +------------------------------------------------------+
 
REGIMES
  [R1] epistemic_model_regime
  [R2] common_knowledge_regime
  [R3] agreement_theorem_regime
  [R4] formalization_regime
 
TENSIONS
  [T1] informal_vs_formal_reasoning      (R1/R3 <--> R4)
  [T2] intuitive_vs_symbolic_epistemics  (R1 <--> R2)
  [T3] local_beliefs_vs_global_structure (R1/R2 <--> R3)
 
TRANSITIONS
  [X1] informal_to_formal_transition
  [X2] epistemic_to_modal_transition
  [X3] local_posterior_to_global_agreement_transition
 
FLOW
  epistemic_model_regime (R1)
        |
        v
  common_knowledge_regime (R2)
        |
        v
  agreement_theorem_regime (R3)
        |
        v
  formalization_regime (R4)
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