3. Comparison with Existing Languages

3.1 Overview of Related Languages and Frameworks

MOISE+: A structural, functional, and deontic description model for organizational multi-agent systems [Hübner+, 2007]. Can formally describe organizational roles, groups, and missions, but contracts and algorithms are outside scope.

OperA: An organizational model for agent-based systems [Dignum, 2004]. Describes organizations from three perspectives: social structure, interaction structure, and normative structure. Has some protocol description support, but does not address SoS institutional layer.

Symboleo: A formal specification language for legal contracts [Sharifi+, 2020]. Can precisely describe contract parties, obligations, rights, and violation conditions, but integration with organizational structure, protocols, and technical architecture is outside scope.

AADL Contract Extension: An extension of Architecture Analysis and Design Language [Feiler & Gluch, 2012] that introduces contract concepts. Integrates assume-guarantee contracts into architecture descriptions, but does not target SoS institutional layer in design.

SysMLv2 / HAMR: Next-generation system modeling language [OMG, 2025], and a model-driven code generation toolchain that originated for AADL and also targets SysMLv2 [Hatcliff+, 2021]. Excellent for architecture description, but institutional design variables are outside scope.

Smart Contracts (Solidity, etc.): Implementation platform for distributed self-governance; Solidity [Solidity Documentation] is a representative language, and a finite-state-machine-based design method for secure contracts has been proposed [Mavridou & Laszka, 2018]. Promising for C-SoS governance implementation, but does not provide verification at design stage or three-layer integrated description.

IAD Framework: Ostrom's Institutional Analysis and Development framework [Ostrom, 2005]. Conceptually analyzes governance of shared resources, but is not a formal description language and parametrization is limited.

3.2 Comparative Analysis

The table below organizes how existing approaches address requirements needed for SoS institutional design. Legend: ◎=Core feature, ○=Partial support, △=Limited, ×=Out of scope. The ratings reflect the authors' reading of each language's specification and of the literature in Appendix B. The CADL column shows the intended scope of the language design; it does not mean that the current reference implementation already provides every item.

Requirement	MOISE+	OperA	Symboleo	AADL Ext.	SysMLv2	Smart Contracts	CADL (This Language)
Organization structure description	◎	○	×	○	◎	×	◎
Contract description	×	×	◎	△	×	◎	◎
Protocol description	△	○	×	△	△	△	◎
Algorithm reference	×	×	×	○	○	△	◎
SoS institutional parametrization	×	×	△	×	×	×	◎
Dynamic institutional switching	×	×	×	×	×	×	◎
Formal verification	△	△	○	◎	△	△	◎
Runtime monitoring	△	△	×	△	×	◎	◎
Environment modeling	×	×	×	△	○	×	◎
AI integration	×	×	×	×	×	△	◎

3.3 Uniqueness of CADL

Within the scope of our survey, we found no existing approach that alone satisfies all requirements. CADL's distinguishing features are summarized in three points:

(1) Three-layer integrated description: CADL consistently describes three layers within a single language: institutions (authority, incentives, information sharing), protocols (coordination procedures, timing constraints), and algorithms (abstract references to computational methods). Within the scope of our survey, we found no existing DSL that covers all three layers in one language.

(2) Parametric institutional design: Directly supports regime map construction by defining institutional design variables such as decision centralization degree (β), information sharing degree (α), and incentive intensity (λ) as numerical parameters.

(3) Unified describe-verify-deploy-monitor cycle: Aims to support formal verification at design stage (consistency and safety), code generation at deployment, and runtime monitoring at operation, all on a unified language foundation.