Graph-of-Thought

Scenario 1

Contradiction (basketball sandbox)

A goal, a solution, and two constraints. One relation is CONTRADICTS — the graph is invalid.

Invalid

Contradictions1

Thoughts4

Relations3

flowchart LR
    n0["I want to play basketball
goal · 0.30"]
    n1["I have a basketball
solution · 0.20"]
    n2["I love basketball
constraint · 0.80"]
    n3["I love sports
constraint · 0.80"]
    n0 -->|requires| n1
    n1 -->|depends_on| n2
    n2 -.->|contradicts| n3

What the engine found

Direct contradiction: I love basketball CONTRADICTS I love sports

Some paths exist but the reasoning contains inconsistencies.

Relations

I want to play basketball requires I have a basketball
I have a basketball depends_on I love basketball
I love basketball contradicts I love sports

Confidence after propagation

Thought	Type	Belief	Change
I want to play basketball	goal	0.30	0.30
I have a basketball	solution	0.20	0.20
I love basketball	constraint	0.80	0.80
I love sports	constraint	0.80	0.80

Raw GraphDTO / Mermaid

{
  "nodes": [
    {
      "id": "c2450db3-1376-4723-b0ac-d08d3854b7cf",
      "concept": "I want to play basketball",
      "node_type": "goal",
      "confidence": 0.3,
      "metadata": {}
    },
    {
      "id": "754d3d18-78c0-4aa4-9861-c93b3c69b80b",
      "concept": "I have a basketball",
      "node_type": "solution",
      "confidence": 0.2,
      "metadata": {}
    },
    {
      "id": "28957ad5-6ba7-4fc0-ab0e-ae2d37ec7f84",
      "concept": "I love basketball",
      "node_type": "constraint",
      "confidence": 0.8,
      "metadata": {}
    },
    {
      "id": "fbbdf506-cfc0-4f69-a667-7f5a7b67b653",
      "concept": "I love sports",
      "node_type": "constraint",
      "confidence": 0.8,
      "metadata": {}
    }
  ],
  "edges": [
    {
      "source_id": "c2450db3-1376-4723-b0ac-d08d3854b7cf",
      "target_id": "754d3d18-78c0-4aa4-9861-c93b3c69b80b",
      "relation_type": "requires",
      "confidence": 0.5,
      "metadata": {}
    },
    {
      "source_id": "754d3d18-78c0-4aa4-9861-c93b3c69b80b",
      "target_id": "28957ad5-6ba7-4fc0-ab0e-ae2d37ec7f84",
      "relation_type": "depends_on",
      "confidence": 0.5,
      "metadata": {}
    },
    {
      "source_id": "28957ad5-6ba7-4fc0-ab0e-ae2d37ec7f84",
      "target_id": "fbbdf506-cfc0-4f69-a667-7f5a7b67b653",
      "relation_type": "contradicts",
      "confidence": 0.5,
      "metadata": {}
    }
  ],
  "metadata": {}
}

flowchart LR
    n0["I want to play basketball<br/>goal · 0.30"]
    n1["I have a basketball<br/>solution · 0.20"]
    n2["I love basketball<br/>constraint · 0.80"]
    n3["I love sports<br/>constraint · 0.80"]
    n0 -->|requires| n1
    n1 -->|depends_on| n2
    n2 -.->|contradicts| n3

Scenario 2

Epistemic propagation (rain → wet grass)

Rain supports wet grass. Epistemic propagation raises belief in the supported node.

Valid

Contradictions0

Thoughts2

Relations1

flowchart LR
    n0["Rain
fact · 0.90"]
    n1["Wet grass
concept · 0.60"]
    n0 -->|supports| n1

What the engine found

No structural violations.

Some paths exist but the reasoning contains inconsistencies.

Relations

Rain supports Wet grass

Confidence after propagation

Thought	Type	Belief	Change
Rain	fact	0.90	0.90
Wet grass	concept	0.60	↑ 0.50 → 0.60

Raw GraphDTO / Mermaid

{
  "nodes": [
    {
      "id": "68d0777a-8117-4593-bb14-4fc67db46ba0",
      "concept": "Rain",
      "node_type": "fact",
      "confidence": 0.9,
      "metadata": {}
    },
    {
      "id": "f9235061-602a-451f-b104-c538ec8f97e7",
      "concept": "Wet grass",
      "node_type": "concept",
      "confidence": 0.6,
      "metadata": {}
    }
  ],
  "edges": [
    {
      "source_id": "68d0777a-8117-4593-bb14-4fc67db46ba0",
      "target_id": "f9235061-602a-451f-b104-c538ec8f97e7",
      "relation_type": "supports",
      "confidence": 0.5,
      "metadata": {}
    }
  ],
  "metadata": {}
}

flowchart LR
    n0["Rain<br/>fact · 0.90"]
    n1["Wet grass<br/>concept · 0.60"]
    n0 -->|supports| n1