Intermediary Artifact Models

• Intermediary artifact models are formally defined frameworks that represent the structure, state, and transformation of artifacts across diverse systems.
• They employ computational methods such as UML state machines, symbolic verification, and fragment anchoring to ensure consistency and tractability.
• Applications range from business process mining to medical imaging, improving system integration and quantitative performance metrics.

Intermediary artifact models formalize the representations, structures, and transformation processes that mediate between distinct states, fragments, or types of artifacts across workflows, lifecycle models, or engineering systems. Serving as both semantically precise connectors (for knowledge, process, or data exchange) and as explicit computational objects (for verification, mining, or transformation), intermediary artifact models have applications spanning business processes, information systems, model-driven engineering, and medical imaging. Their theoretical underpinnings and practical realizations are grounded in a range of formal and computational frameworks.

1. Formal Definitions and Structural Properties

Intermediary artifact models are precisely characterized in several domains by their formalization of structure, state, and transformation.

• Business Processes: In artifact-centric business process modeling, intermediary artifacts are defined as UML classes with explicit state hierarchies (subclass lattices) and lifecycle state-machines. The state space is constructed over subclasses, representing intermediate states that an artifact transitions through before termination. The class diagram $$M = (C, R, \leq, src, tgt, mult_1, mult_2, role_1, role_2)$$, with $artifacts \subseteq C$ distinguished and $a$-classes$:(A) = \{S \in C \mid S\leq^*A, S \text{ leaf}\}$, underlies both the artifact's structure and its intermediary states (Calvanese et al., 2014).
• Symbolic Artifact Systems: Tuple Artifact Systems (TAS) formalize an intermediary representation for verifying Guard-Stage-Milestone (GSM) processes. A TAS $\Gamma = \langle DB, \vec{x}, \Sigma, \Pi \rangle$ models artifact variables, actions (services), and a data schema, supporting a symbolic abstraction that encodes process runs and artifact state transitions (Li et al., 2017).
• Multi-Artifact Engineering: In model-driven engineering and interactive system design, intermediary artifact models are the intermediate artifacts—task models, dialog models, UI sketches, prototypes—produced at each iteration, each providing complementary partial views. The systematic linkage and exchange of information between these heterogeneous models is achieved using a formally specified annotation model that treats annotations as first-class, cross-model entities (Winckler et al., 2022).
• Information Fragments: The General Fragment Model (GFM) defines intermediary structures for anchoring semantic descriptions to arbitrary fragments within information artifacts. Using a formalism of indexers and anchors, fragments can be specified and referenced in a vocabulary-agnostic way, supporting systematic linking across heterogeneous artifacts (Fiorini et al., 2019).

2. Methodological and Computational Frameworks

The construction, operation, and verification of intermediary artifact models leverage well-defined algorithms and symbolic representations.

• Artifact Lifecycle Discovery: The pipeline for mining artifact lifecycles decomposes raw event logs into a sequence of intermediate models: relational (ER) models, entity-relationship mining, artifact identification, artifact-centric event logs, workflow Petri nets, and declarative Guard-Stage-Milestone models. Each step produces an intermediary model amenable to standard analysis techniques (FD/IND discovery, relational algebra, Petri-net mining) and systematic mapping to higher-level lifecycle representations (Popova et al., 2013).
• Symbolic Verification: The compilation of GSM workflows into TAS (in SpinArt) yields a symbolic transition system encoding artifact states and transitions as isomorphism types and service actions. Promela code generation and optimizations such as Lazy Dependency Tests and Assignment Set Minimization enable tractable, complete, and PSPACE-complete model checking (Li et al., 2017).
• Annotation Propagation: In multi-artifact engineering, the propagation and synchronization of annotations across intermediary artifact models rely on model-to-model mappings, selector functions, and consistency checkers. The meta-model $(id, b, Targets, sel, \tau, c, md)$ parameterizes annotations by target models, element selectors, type/motivation, and metadata, ensuring consistency and traceability across artifact evolution (Winckler et al., 2022).
• Fragment Model Operations: GFM supports composition of indexers for constructing fragments-of-fragments, typing and composing anchors, and embedding constraints relevant for reasoning (e.g., interval overlap). Such operations formalize how semantic queries, annotations, or links can systematically address substructures of complex artifacts (Fiorini et al., 2019).

3. Semantics and Linking Mechanisms

Intermediary artifact models are distinguished by mechanisms for referencing, associating, and ensuring consistency across fragments or states in heterogeneous artifacts.

• Anchoring and Selectors: Semantics are systematically linked to artifacts via anchors—that is, the result of applying an indexer (e.g., time interval, XPath, region selection) to a concrete token tuple. Selector functions are domain-specialized (widget IDs, task IDs, Petri-net transitions, bit positions) and support composition, type-safety, and dynamic re-anchoring during version evolution (Fiorini et al., 2019, Winckler et al., 2022).
• Cross-Model Annotation: Annotations act as intermediary artifacts themselves, referencing multiple models and their elements, and propagating rationale, requirements, or decisions through formal model-to-model mappings and centrally managed repositories (Winckler et al., 2022).
• Composite Artifact Laws: In explicit artifact models for imaging (e.g., AF2R for MRI), nonlinear composite laws model the coupling between underlying structure and superposed artifacts. For instance, $I(x) = J(x) + R(x) - \lambda [J(x) * R(x)]$ encodes the structured overlay of motion artifacts atop anatomical signals, enabling reversible and interpretable transformations in the artifact removal process (Su et al., 2023).

4. Applications in Process, System, and Data Domains

Intermediary artifact models have diverse applications, each leveraging their logical, structural, and operational properties.

• Business Process Verification: By modeling artifact-centric processes (e.g., Orders) as UML class diagrams and state machines, and encoding lifecycles as state transitions over intermediary states, one can specify and check FO-temporal properties such as reachability, progress, and state invariants. Decidability is achieved by constraining OCL expressions (navigational, unidirectional), bounding cardinalities, and limiting sharing (Calvanese et al., 2014).
• Process Mining: Artifact lifecycle discovery pipelines extract intermediary artifact models at multiple abstraction stages, enabling the reuse of classical entity and process discovery methods, scalable decomposition, and modular synthesis of declarative GSM models (Popova et al., 2013).
• Interactive System Engineering: Intermediary artifact models are critical for integrating heterogeneous models (task, dialogue, UI), facilitating traceability, coordinated evolution, and rigorous documentation of design rationale via annotation models and supporting tool suites (Winckler et al., 2022).
• Information Fragmentation and Semantics: GFM enables the systematic anchoring of conceptual, ontological, or semantic descriptions to data fragments—ranging from seismic cubes to multimedia timelines or XML subtrees. This model-independent anchoring supports query optimization, inference, and heterogeneous interoperation (Fiorini et al., 2019).
• Medical Imaging: Physics-inspired intermediary artifact models, such as AF2R, formalize and preserve the structured dependency between artifacts and anatomy, facilitating interpretable, likelihood-based removal procedures that outperform implicit (GAN-based) restoration techniques (Su et al., 2023).

5. Quality, Decidability, and Computational Guarantees

The design of intermediary artifact models is strongly influenced by requirements for tractability, semantic faithfulness, and operational guarantees.

• State Boundedness and Decidability: In artifact-centric process verification, modeling constraints—navigational OCL, unidirectionality, cardinality bounds, and sharing via read-only data—yield state-bounded data-centric dynamic systems. This permits finite-state abstractions and FO-temporal model checking (μ-calculus, LTL/CTL) (Calvanese et al., 2014).
• PSPACE-Complete Verification: For workflow artifact systems encoded as TAS, LTL-FO model checking is proven PSPACE-complete, with optimizations enabling verification of workflows with dozens of artifacts and services in seconds (Li et al., 2017).
• Quantitative and Qualitative Performance: In artifact removal from MR images, explicit intermediary models achieve higher PSNR and SSIM scores than GAN or CNN baselines. For example, AF2R achieves PSNR/SSIM of $47.6/0.99$ (fat-suppressed), $46.1/0.99$ (DualEcho), and $46.1/0.99$ (water-fat separable), preserving anatomical details and eliminating artifacts more effectively than implicit models (Su et al., 2023).
• Scalability and Modularity: Modular pipelines for artifact lifecycle discovery and fragment model composition support direct application of standard mining and reasoning tools, avoiding combinatorial blow-up and facilitating parallelizable, manageable computation (Popova et al., 2013, Fiorini et al., 2019).

6. Limitations, Extensions, and Open Directions

Despite their expressive power, intermediary artifact models present challenges and promising extensions.

• Annotation Model Integration: Current implementations require integration of plugins into each model editor and manual specification of model-to-model mappings; scaling and automating these linkages and maintaining selector validity as artifacts evolve remain open technical areas (Winckler et al., 2022).
• Empirical Scalability: While GFM offers a theoretically complete scaffold for fragment anchoring, large-scale empirical validation on Big Data and more complex indexers (e.g., semantic segmentation pipelines) are pending (Fiorini et al., 2019).
• Expressivity vs. Decidability: Enabling more expressive linkages (e.g., artifacts sharing mutable data or supporting global OCL queries) may compromise decidability or require additional bounding strategies (Calvanese et al., 2014).
• Explicit vs. Implicit Models: Explicit intermediary artifact models provide interpretability, density control, and exactness (e.g., normalizing flows in AF2R), but may require greater domain knowledge for specification compared to implicit (adversarial) models; the trade-off between transparency, learnability, and domain-fitness is domain-specific (Su et al., 2023).
• Ontology and Tooling Integration: Further development is needed to automate model-to-model mappings (e.g., via ATL or machine-readable ontologies), enforce annotation consistency (rule engines), and integrate annotation repositories as first-class web services (Winckler et al., 2022).

7. Comparative Summary Across Domains

Domain	Intermediary Model	Core Formalism
Business process verification	UML artifact with lifecycles	Class diagram, state machine
Workflow verification	Tuple Artifact System (TAS)	Symbolic transitions, FO logic
Multi-artifact engineering	Annotation meta-model	Set-theoretic tuples, selectors
Information fragment anchoring	General Fragment Model (GFM)	Indexers/anchors, set theory
Imaging artifact correction	Artifact-free flow (AF2R)	Physics-inspired nonlinear law, flow

Each approach leverages intermediary artifact models to enforce rigor, enable compositionality, and bridge heterogeneity, ensuring that complex systems and datasets can be analyzed, verified, and integrated in a semantically meaningful and computationally tractable manner (Calvanese et al., 2014, Li et al., 2017, Winckler et al., 2022, Fiorini et al., 2019, Popova et al., 2013, Su et al., 2023).