IndisputableMonolith.Ethics.StakeGraph
The StakeGraph module introduces formal definitions for stakeholders and their relational graphs within the Ethics domain of Recognition Science. It defines Stakeholder as a label type and StakeGraph as a structure supporting containment checks, neighbor relations, reachability, mutual reachability, and cycle detection. Formal ethicists and decision theorists would reference these when modeling multi-agent ethical scenarios. As a foundational module, it consists entirely of definitions with no theorems or proofs.
claimThe module defines $Stakeholder$ as a label and $StakeGraph$ as a graph on stakeholders equipped with predicates $contains$, $neighbors$, $reachable$, $mutualReachable$, and $hasCycle$.
background
This module operates in the Ethics subdomain of Recognition Science, importing only Mathlib for basic structures. It introduces Stakeholder as a type representing entities with interests or stakes. StakeGraph models interactions as a directed or undirected graph. The sibling definitions provide graph-theoretic operations: contains verifies if a stakeholder is in the graph, neighbors lists adjacent stakeholders, reachable determines if one can be reached from another, mutualReachable checks bidirectional reachability, and hasCycle detects the presence of cycles in the graph.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies core data structures for ethical graph modeling in Recognition Science. It feeds into broader ethics theorems concerning stakeholder alignment and decision processes, though specific parent theorems are not yet linked in the dependency graph. It establishes the formal language for analyzing ethical networks using graph properties.
scope and limits
- Does not assign numerical weights or utilities to stakeholders.
- Does not incorporate Recognition Science constants such as phi or J-cost.
- Does not prove any properties of the graph structures.
- Does not define ethical axioms or decision rules.