## Analysis of inconsistency in graph-based viewpoints (2003)

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Venue: | In ASE |

Citations: | 29 - 11 self |

### BibTeX

@INPROCEEDINGS{Sabetzadeh03analysisof,

author = {Mehrdad Sabetzadeh and Steve Easterbrook},

title = {Analysis of inconsistency in graph-based viewpoints},

booktitle = {In ASE},

year = {2003},

pages = {12--21}

}

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### Abstract

Eliciting the requirements for a proposed system typically involves different stakeholders with different expertise, responsibilities, and perspectives. Viewpoints-based approaches have been proposed as a way to manage incomplete and inconsistent models gathered from multiple sources. In this paper, we propose a category-theoretic framework for the analysis of fuzzy viewpoints. Informally, a fuzzy viewpoint is a graph in which the elements of a lattice are used to specify the amount of knowledge available about the details of nodes and edges. By defining an appropriate notion of morphism between fuzzy viewpoints, we construct categories of fuzzy viewpoints and prove that these categories are (finitely) cocomplete. We then show how colimits can be employed to merge the viewpoints and detect the inconsistencies that arise independent of any particular choice of viewpoint semantics. We illustrate an application of the framework through a case-study showing how fuzzy viewpoints can serve as a requirements elicitation tool in reactive systems. 1

### Citations

1175 |
Introduction to Lattices and Order
- Davey, Priestley
- 1990
(Show Context)
Citation Context ...rder is a reflexive, antisymmetric, and transitive binary relation. A non-empty set with a partial order on it is called a partially ordered set or a poset, for short. We use Hasse diagrams (cf. e.g. =-=[5]-=-) to visualize finite posets. Definition 2.3 Let Q be a poset. An element ⊤ ∈ Q is said to be the top element if ∀a ∈ Q : a ≤ ⊤. Dually, an element ⊥ ∈ Q is said to be the bottom element if ∀a ∈ Q : ⊥... |

419 |
Category Theory for Computer Science
- Barr, Wells
- 1990
(Show Context)
Citation Context ...theory and only review diagrams, colimits, and comma categories in order to provide context and establish notation. An excellent introduction to category theory from a computer science perspective is =-=[1]-=-. Detailed discussion about comma categories can be found in [13, 16]. 2.3.1 Diagrams and Colimits Definition 2.8 A (finite) diagram D in a category C consists of: a (finite) graph G(D); a C -object D... |

318 |
A useful four-valued logic
- Belnap
- 1977
(Show Context)
Citation Context ...ead to a definition for syntactic inconsistency based on colimits. The simplest and maybe the most widely used lattice capable of modeling uncertainty and disagreement is Belnap’s four-valued lattice =-=[2]-=- which was earlier referred to as A4. In A4, every value shows a possible “amount of knowledge” available about a concept. The value M (i.e. MAYBE) denotes a lack of information, T (i.e. TRUE) and F (... |

106 | Using viewpoints for inconsistency management
- Easterbrook, Nuseibeh
- 1996
(Show Context)
Citation Context ...eteness and inconsistency within a viewpoint cannot be modeled explicitly. Consistency checking is achieved by expressing a set of consistency rules in a rich meta-language, such as first order logic =-=[8, 7]-=-. With this approach, viewpoints can be merged only by making them consistent first, and then using classical composition operators. Alternatively, one could translate a set of viewpoints, together wi... |

105 | A categorical manifesto
- Goguen
- 1991
(Show Context)
Citation Context ...per builds upon the category-theoretic properties of fuzzy sets noted in [10, 11]. The use of colimits as an abstract mechanism for putting structures together has been known for quite some time (cf. =-=[12]-=- for references). In [14, 15], colimits have been used for merging viewpoints. In that approach, viewpoints are described by open graph transformation systems and colimits are used to integrate them. ... |

78 | A framework for multi-valued reasoning over inconsistent viewpoints
- Easterbrook, Chechik
- 2001
(Show Context)
Citation Context ...ces [8]. We may use viewpoints to specify different features of a system, describe different perspectives on a single functionality, or model individual processes that need to be composed in parallel =-=[6]-=-. By separating the descriptions provided by different stakeholders, viewpoints-based approaches facilitate the detection of inconsistencies between the descriptions. In the classical viewpoint approa... |

57 |
Computational Category Theory
- Rydeheard, Burstall
- 1988
(Show Context)
Citation Context ...in order to provide context and establish notation. An excellent introduction to category theory from a computer science perspective is [1]. Detailed discussion about comma categories can be found in =-=[13, 16]-=-. 2.3.1 Diagrams and Colimits Definition 2.8 A (finite) diagram D in a category C consists of: a (finite) graph G(D); a C -object Dn for each node n in G(D); and a C -morphism De : D sG(D)(e) → D tG(D... |

50 |
Bits and pieces of the theory of institutions
- Tarlecki
- 1986
(Show Context)
Citation Context ...′ . ) f ′ Identities are pairs of identities and composition is defined component-wise, i.e. for a pair of morphisms (s, t) and (s′, t ′), we have: (s, t) ◦(s ′, t ′) = (s ◦ s ′, t ◦ t ′). Lemma 2.16 =-=[19, 16]-=- Let L : A → C and R : B → C be functors with L (finitely) cocontinuous. If A and B are (finitely) cocomplete so is the comma category (L ↓ R). A remarkable fact about colimit construction in (L ↓ R) ... |

43 | Constructing specification morphisms
- Smith
- 1993
(Show Context)
Citation Context ...t binds to this shared vocabulary. Alternatively, we anticipate that the limitation could be addressed by introducing explicit signatures and signature morphisms, similar to the approach described in =-=[18]-=-; however, we have not yet investigated this idea. 5 Viewpoint Integration and Characterization of Inconsistency It is well-known that “for a given species of structure, say widgets, the result of int... |

41 |
Kleene’s logic, generalized
- Fitting
- 1990
(Show Context)
Citation Context ...hat results from removing the top element from A4 (resp. A10) together with the associated truth ordering in Figure 6a (resp. 6b) is an instance of a family of multivalued logics known as Kleene-like =-=[9]-=- logics. In this paper, we shall only appeal to the intuitive nature of such logics and therefore, omit the formal procedure for constructing them. The interested reader should refer to [9] for furthe... |

24 |
Some fundamental algebraic tools for the semantics of computation–part 1: Comma categories, colimits, signatures and theories
- Goguen, Burstall
- 1984
(Show Context)
Citation Context ...in order to provide context and establish notation. An excellent introduction to category theory from a computer science perspective is [1]. Detailed discussion about comma categories can be found in =-=[13, 16]-=-. 2.3.1 Diagrams and Colimits Definition 2.8 A (finite) diagram D in a category C consists of: a (finite) graph G(D); a C -object Dn for each node n in G(D); and a C -morphism De : D sG(D)(e) → D tG(D... |

23 |
Concept representation in natural and artificial languages: Axioms, extensions and applications for fuzzy sets
- Goguen
- 1974
(Show Context)
Citation Context ...ed with the additional structures required for modeling incompleteness and inconsistency. The mathematical machinery in this paper builds upon the category-theoretic properties of fuzzy sets noted in =-=[10, 11]-=-. The use of colimits as an abstract mechanism for putting structures together has been known for quite some time (cf. [12] for references). In [14, 15], colimits have been used for merging viewpoints... |

12 |
et al. Inconsistency handling in multiperspective specifications
- Finkelstein
- 1994
(Show Context)
Citation Context ...ies to express their descriptions, and have conflicting goals. Viewpoints-based approaches have been proposed as a way to manage incomplete and inconsistent information gathered from multiple sources =-=[8]-=-. We may use viewpoints to specify different features of a system, describe different perspectives on a single functionality, or model individual processes that need to be composed in parallel [6]. By... |

11 | Model Checking with Multi-Valued Temporal Logics
- Chechik, Easterbrook, et al.
- 2001
(Show Context)
Citation Context ...nd so on. The existence of such truth ordering lattices is an advantage when we want to interpret viewpoints according to certain semantics. For example, we may want to treat a viewpoint as a χKripke =-=[3]-=- structure and verify certain temporal properties in it through multivalued model-checking [3]. For such an application, we are naturally interested in measuring the “amount of truth” for the desired ... |

5 | Category Theory for Computing Science. Les Publications CRM, Montréal, third edition, 1999. Alessandra Carbone. Interpolants, cut elimination and flow graphs for the propositional calculus. Annals of Pure and Applied Logic - Barr, Wells - 1997 |

5 |
Stochastic graph transformation systems
- Heckel, Lajios, et al.
(Show Context)
Citation Context ...ory-theoretic properties of fuzzy sets noted in [10, 11]. The use of colimits as an abstract mechanism for putting structures together has been known for quite some time (cf. [12] for references). In =-=[14, 15]-=-, colimits have been used for merging viewpoints. In that approach, viewpoints are described by open graph transformation systems and colimits are used to integrate them. Our work is, as far as we kno... |

4 |
et al., Algebraic Approaches to Graph Transformation Part 1: Basic Concepts and Double Pushout Approach
- Corradini, Montanari, et al.
- 1997
(Show Context)
Citation Context ...work that will involve several casestudies. Another interesting subject is using the framework presented in this paper for developing graph transformation systems based on the double-pushout approach =-=[4]-=-. In [17], some initial steps have been taken in this direction, but further work remains to be done. Acknowledgments. We thank Wolfram Kahl for his extensive help in improving this paper, Andrzej Tar... |

4 |
Categories of Fuzzy Sets: Applications of a Non-Cantorian Set Theory
- Goguen
- 1968
(Show Context)
Citation Context ...ed with the additional structures required for modeling incompleteness and inconsistency. The mathematical machinery in this paper builds upon the category-theoretic properties of fuzzy sets noted in =-=[10, 11]-=-. The use of colimits as an abstract mechanism for putting structures together has been known for quite some time (cf. [12] for references). In [14, 15], colimits have been used for merging viewpoints... |

2 | A category-theoretic approach to representation and analysis of inconsistency in graph-based viewpoints
- Sabetzadeh
- 2003
(Show Context)
Citation Context ...uch as types and additional labels through wellknown comma categorical techniques without violating the cocompleteness result achieved in Theorem 4.3. For some preliminary work in this direction, see =-=[17]-=-. A limitation to FView categories which is implicit in the notion of viewpoint morphism is that we assume the existence of a unified universe of atomic propositions (denoted U). This implies that the... |

1 |
et al. A view-based approach to system modeling based on open graph transformation systems
- Heckel
- 1999
(Show Context)
Citation Context ...ory-theoretic properties of fuzzy sets noted in [10, 11]. The use of colimits as an abstract mechanism for putting structures together has been known for quite some time (cf. [12] for references). In =-=[14, 15]-=-, colimits have been used for merging viewpoints. In that approach, viewpoints are described by open graph transformation systems and colimits are used to integrate them. Our work is, as far as we kno... |