Functorial Model Management

PLoS ONE, 2012

In this paper we introduce the olog, or ontology log, a categorytheoretic model for knowledge representation (KR). Grounded in formal mathematics, ologs can be rigorously formulated and cross-compared in ways that other KR models (such as semantic networks) cannot. An olog is similar to a relational database schema; in fact an olog can serve as a data repository if desired. Unlike database schemas, which are generally difficult to create or modify, ologs are designed to be user-friendly enough that authoring or reconfiguring an olog is a matter of course rather than a difficult chore. It is hoped that learning to author ologs is much simpler than learning a database definition language, despite their similarity. We describe ologs carefully and illustrate with many examples. As an application we show that any primitive recursive function can be described by an olog. We also show that ologs can be aligned or connected together into a larger network using functors. The various methods of information flow and institutions can then be used to integrate local and global world-views. We finish by providing several different avenues for future research. Contents 40 7. Further directions 48 References 50 Mathematics, MIT,

With the rise of model-driven software development, more and more development tasks are being performed on models. Seamless exchange of models among different modeling tools increasingly becomes a crucial prerequisite for effective software development processes. Due to lack of interoperability, however, it is often difficult to use tools in combination, thus the potential of model-driven software development cannot be fully utilized. To tackle this problem, we propose ModelCVS, a system aiming at model-based tool integration. ModelCVS enables transparent transformation of models between different tools' languages and exchange formats, as well as versioning exploiting the rich syntax and semantics of models, thus going beyond existing low-level model transformation approaches. For this, ModelCVS utilizes semantic technologies in terms of ontologies and supports different integration patterns at the metamodel level. To foster reuse, a knowledge base captures essential information relevant for tool integration.

International Workshop on Modeling in Software Engineering (MISE'07: ICSE Workshop 2007), 2007

A key problem in model-based development is merging a set of distributed models into a single seamless model. To merge a set of models, we need to know how they are related. In this position paper, we discuss the methodological aspects of describing the relationships between models. We argue that relationships between models should be treated as first-class artifacts in the merge problem and propose a general framework for model merging based on this argument. We illustrate the usefulness of our framework by instantiating it to the state-machine modelling domain and developing a flexible tool for merging state-machines.

Artificial Intelligence: Methodology, Systems, and …, 1998

Due to the increasing necessity and availability of information from di erent sources, information integration is becoming one of the challenging issues in arti cial intelligence and computer science. A successful methodology for information integration is based on federated databases. Di erently form databases, a completely satisfactory formal treatment of federated databases is still missing. The goal of this paper is to ll this gap by providing a model theoretic semantics, called Local Models Semantics for federated databases. Our basic intuition is that a federated database can be formalized by representing each database as a set of local models. We argue that this perspective is a promising one, as many relevant problems in information integration, such as semantic heterogeneity, interschema dependencies, query distribution, local control over data and processing, and transparency, can be successfully represented by Local Models Semantics. ? We thank the Mechanized Reasoning Group at DISA, ITC{IRST and DIST (Univ.

2008

Abstract Model-based development involves construction, integration, and maintenance of complex models. One of the key problems in model-based development is composing a set of distributed models into a single seamless model. In this paper we propose a declarative approach for model composition, which augments and strengthens existing structural and heuristic approaches. In our approach, the desired model compositions are constrained by a set of declarative properties, which drive the merge process.

2012

Specification and maintenance of relationships between models are vital for MDE. We show that a wide class of such relationships can be specified in a compact and precise manner, if intermodel mappings are allowed to link derived model elements computed by corresponding queries. Composition of such mappings is not straightforward and requires specialized algebraic machinery. We present a formal framework, in which such machinery can be defined generically for a wide class of metamodel definitions. This enables algebraic specification of practical intermodeling scenarios, e.g., model merge.

… conference on Very large data bases, 2007

Manipulation of models and mappings is a common task in the design and development of information systems. Research in Model Management aims at supporting these tasks by providing a set of operators to manipulate models and mappings. As a framework, GeRoMeSuite provides an environment to simplify the implementation of model management operators. GeRoMeSuite is based on the generic role based metamodel GeRoMe [10], which represents models from different modeling languages (such as XML Schema, OWL, SQL) in a generic way. Thereby, the management of models in a polymorphic fashion is enabled, i.e. the same operator implementations are used regardless of the original modeling language of the schemas. In addition to providing a framework for model management, GeRoMeSuite implements several fundamental operators such as Match, Merge, and Compose.

The GSDLAB technical reports are published as a means to ensure timely dissemination of scholarly and technical work on a non-commercial basis.

Lecture Notes in Computer Science, 2007

Due to the increased complexity of software development projects more and more systems are described by models. The sheer size makes it impractical to describe these systems by a single model. Instead many models are developed that provide several complementary views on the system to be developed. This however leads to a need for compositional models. This paper describes a foundational theory of model composition in form of an algebra to explicitly clarify different variants and uses of composition, their interplay with the semantics of the involved models and their composition operators.

2006

There is little agreement on terminology in model composition, and even less on key characteristics of a model composition solution. We present three composition frameworks: the Atlas Model Weaver, the Epsilon Merging Language, and the Glue Generator Tool, and from them derive a core set of common definitions. We use this to outline the key requirements of a model composition solution, in terms of language and tool support.

Volume 2: 32nd Computers and Information in Engineering Conference, Parts A and B, 2012

One of the primary goals of the Adaptive Vehicle Make (AVM) program of DARPA is the construction of a modelbased design flow and tool chain, META, that will provide significant productivity increase in the development of complex cyber-physical systems. In model-based design, modeling languages and their underlying semantics play fundamental role in achieving compositionality. A significant challenge in the META design flow is the heterogeneity of the design space. This challenge is compounded by the need for rapidly evolving the design flow and the suite of modeling languages supporting it. Heterogeneity of models and modeling languages is addressed by the development of a model integration language-CyPhysupporting constructs needed for modeling the interactions among different modeling domains. CyPhy targets simplicity: only those abstractions are imported from the individual modeling domains to CyPhy that are required for expressing relationships across sub-domains. This "semantic interface" between CyPhy and the modeling domains is formally defined, evolved as needed and verified for essential properties (such as well-formedness and invariance). Due to the need for rapid evolvability, defining semantics for CyPhy is not a "one-shot" activity; updates, revisions and extensions are ongoing and their correctness has significant implications on the overall consistency of the META tool chain. The focus of this paper is the methods and tools used for this purpose: the META Semantic Backplane. The Semantic Backplane is based on a mathematical framework provided by term algebra and logics, incorporates a tool suite for specifying, validating and using formal structural and behavioral semantics of modeling languages, and includes a library of metamodels and specifications of model transformations.

2012

Abstract A key problem in model-based development is integrating a collection of models into a single, larger, specification as a way to construct a functional system, to develop a unified understanding, or to enable automated reasoning about properties of the resulting system. In this article, we suggest that the choice of a particular model integration operator depends on the inter-model relationships that hold between individual models.

2021

The variety of data is one of the important issues in the era of Big Data. The data are naturally organized in different formats and models, including structured data, semi-structured data, and unstructured data. Prior research has envisioned an approach to abstract multi-model data with a schema category and an instance category by using category theory. In this paper, we demonstrate a system, called MultiCategory, which processes multi-model queries based on category theory and functional programming. This demo is centered around four main scenarios to show a tangible system. First, we show how to build a schema category and an instance category by loading different models of data, including relational, XML, key-value, and graph data. Second, we show a few examples of query processing by using the functional programming language Haskell. Third, we demo the flexible outputs with different models of data for the same input query. Fourth, to better understand the category theoretical structure behind the queries, we offer a variety of graphical hooks to explore and visualize queries as graphs with respect to the schema category, as well as the query processing procedure with Haskell.

2006

Abstract If a modeling task is distributed, it will frequently be necessary to merge models developed by different team members. Existing approaches to model merging make assumptions about the types of model to be merged, and the nature of the relationship between them. This makes it hard to compare approaches. In this paper, we present a manifesto for research on model merging.

… panels and industrial contributions at the …, 2007

This paper aims to bring the benefits of the use of Category Theory to the field of Semantic Web, where the coexistence of intrinsically different models of local knowledge makes difficult the exchanging of information. The paper uses categorical limit and colimit to define operations of breaking and composing ontologies, formalizing usual concepts in ontologies (alignment, merge, integration, matching) and proposing a new operation (the hide operation). The presented set of operations form a useful framework that makes easier the manipulation and reuse of ontologies.