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Cohesion Dynamics (CD)

K-LENS-ES — Event Structure Lens

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Paper K-LENS-ES establishes a representation theorem mapping the Cohesion Dynamics kernel grammar (K-KERN) to event structure semantics — specifically prime, stable, and general event structures.

Summary

Event structures provide a well-established mathematical framework for modeling concurrency, causality, and conflict. K-LENS-ES demonstrates that K-KERN grammar can be represented within this framework under explicitly stated additional assumptions, particularly conflict heredity and enabling locality.

This mapping positions CD as a semantic unification of concurrency formalisms, showing how K-KERN subsumes event structure semantics as a special case.

Key Results

  1. K-KERN resolutions map to event structure events under explicit correspondence rules
  2. K-KERN dependency maps to event structure causality preserving acyclicity
  3. K-KERN irreconcilability maps to event structure conflict under conflict heredity assumption
  4. K-KERN admissibility maps to event structure enabling under locality constraints
  5. K-KERN histories map to event structure configurations (consistent, downward-closed event sets)

Status

  • Paper ID: K-LENS-ES
  • Series: K-series (Kernel Grammar & Invariants)
  • Subseries: K-LENS (Semantic Lenses)
  • Status: Staging
  • Dependencies: K-KERN, K-GOV, K-LENS-ORD (informative)

Epistemic Status

Conditional necessity per K-GOV: Event structure representation has been required in explored CD models for concurrency reasoning. No claim of logical necessity or ontological primacy.

Event Structure Variants

General Event Structures

K-KERN subsumes general event structure semantics directly. Every K-KERN kernel can be represented as a general event structure.

Stable Event Structures

Require additional assumptions:

  • Conflict heredity (inherited irreconcilability)
  • Set-based enabling interpretation

Prime Event Structures

Require strong additional assumptions:

  • Conflict heredity
  • Finite causes
  • Unique minimal enabling

Concurrency Semantics

K-LENS-ES shows that K-KERN naturally supports:

  • True concurrency (not just interleaving)
  • Causality (dependency as partial order)
  • Conflict (irreconcilability as symmetric relation)
  • Branching (structural divergence)

Read the Full Paper

See Also

Background: Event Structures

Event structures are a mathematical framework for modeling concurrent systems developed by Winskel, Nielsen, and others. They provide:

  • Events (atomic occurrences)
  • Causality (partial order on events)
  • Conflict (symmetric, irreflexive, inherited relation)
  • Configurations (consistent, downward-closed event sets)

K-LENS-ES shows how these components correspond naturally to K-KERN primitives.